<div class="xblock xblock-public_view xblock-public_view-vertical" data-init="VerticalStudentView" data-has-score="False" data-runtime-version="1" data-graded="False" data-usage-id="block-v1:MITx+24.118x+2T2020+type@vertical+block@5ec57c3fa8374902b2da77f8f9adcf2b" data-runtime-class="LmsRuntime" data-block-type="vertical" data-request-token="8c3580a8035811efb61a02329aca76dd" data-course-id="course-v1:MITx+24.118x+2T2020">
<h2 class="hd hd-2 unit-title">Causal Decision Theory</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+24.118x+2T2020+type@html+block@cbb92747ff4b41e3b5a8eb0ddf9f19cc">
<div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-init="XBlockToXModuleShim" data-has-score="False" data-runtime-version="1" data-graded="False" data-usage-id="block-v1:MITx+24.118x+2T2020+type@html+block@cbb92747ff4b41e3b5a8eb0ddf9f19cc" data-runtime-class="LmsRuntime" data-block-type="html" data-request-token="8c3580a8035811efb61a02329aca76dd" data-course-id="course-v1:MITx+24.118x+2T2020">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "HTMLModule"}
</script>
<p><span style="font-size: 12pt; font-family: 'book antiqua', palatino;"> A decision theory based on the the definition of expected value I gave in Lecture 5.2.2, tells us that the right thing to do in a Newcomb case is to one-box. So if you are a two-boxer, you must think that that form of decision theory is incorrect. In the next few units I’ll tell you how to develop an alternative.</span></p>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-init="VerticalStudentView" data-has-score="False" data-runtime-version="1" data-graded="False" data-usage-id="block-v1:MITx+24.118x+2T2020+type@vertical+block@1818d14d7af14fdd8c71a153c4d9fd81" data-runtime-class="LmsRuntime" data-block-type="vertical" data-request-token="8c3580a8035811efb61a02329aca76dd" data-course-id="course-v1:MITx+24.118x+2T2020">
<h2 class="hd hd-2 unit-title">Dependence, Causal and Probabilistic</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+24.118x+2T2020+type@html+block@5bb1c0d869b945588a673a281c41241d">
<div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-init="XBlockToXModuleShim" data-has-score="False" data-runtime-version="1" data-graded="False" data-usage-id="block-v1:MITx+24.118x+2T2020+type@html+block@5bb1c0d869b945588a673a281c41241d" data-runtime-class="LmsRuntime" data-block-type="html" data-request-token="8c3580a8035811efb61a02329aca76dd" data-course-id="course-v1:MITx+24.118x+2T2020">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "HTMLModule"}
</script>
<p><span style="font-family: 'book antiqua', palatino;">It is useful to start by distinguishing between <em>causal</em> dependence and <em>probabilistic</em> dependence.</span></p>
<ul>
<li>
<p><span style="font-family: 'book antiqua', palatino;">Two events are <strong>causally independent</strong> if neither of them is a cause of the other; otherwise, the effect is <strong>causally dependent</strong> on the cause.</span></p>
</li>
<li>
<p><span style="font-family: 'book antiqua', palatino;">Two events are <strong>probabilistically independent</strong> if the assumption that one of them occurs does not affect the probability that the other one will occur; otherwise, each of them is <strong>probabilistically dependent</strong> on the other.</span></p>
</li>
</ul>
<p><span style="font-family: 'book antiqua', palatino;">The umbrella example can be used to illustrate the difference between these two types of dependence:</span></p>
<ul>
<li>
<p><span style="font-family: 'book antiqua', palatino;">There being wet sidewalks is <em>probabilistically dependent</em> on umbrella use, because the assumption that people are using umbrellas increases the probability of wet sidewalks.</span></p>
</li>
<li>
<p><span style="font-family: 'book antiqua', palatino;">There being wet sidewalks is <em>causally independent</em> of umbrella use, because umbrella use does not <em>cause</em> sidewalks to be wet and wet sidewalks do not cause umbrella use. (What we have instead is a <em>common cause</em>: rain causes both wet sidewalks and umbrella use.)</span></p>
</li>
</ul>
<p><span style="font-family: 'book antiqua', palatino;">Something similar happens in the case of Newcomb’s Problem:</span></p>
<ul>
<li>
<p><span style="font-family: 'book antiqua', palatino;">Whether or not the large box contains a million dollars is <em>probabilistically dependent</em> on your choice to one-box or two-box, because the assumption that you one-box increases the probability that the large box contains the money. </span></p>
</li>
<li>
<p><span style="font-family: 'book antiqua', palatino;">Whether or not the large box contains a million dollars it is <em>causally independent</em> from your choice to one-box or two-box, because your action doesn’t cause the box to have the money in it, and the amount of money in the box does not cause your action. (Here too we have a <em>common cause</em>: your psychological constitution causes both your decision and the predictor’s prediction.)</span></p>
</li>
</ul>
</div>
</div>
<div class="vert vert-1" data-id="block-v1:MITx+24.118x+2T2020+type@problem+block@59d40e705d334deaaebc538ea767c3c7">
<div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-init="XBlockToXModuleShim" data-has-score="True" data-runtime-version="1" data-graded="False" data-usage-id="block-v1:MITx+24.118x+2T2020+type@problem+block@59d40e705d334deaaebc538ea767c3c7" data-runtime-class="LmsRuntime" data-block-type="problem" data-request-token="8c3580a8035811efb61a02329aca76dd" data-course-id="course-v1:MITx+24.118x+2T2020">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_59d40e705d334deaaebc538ea767c3c7" class="problems-wrapper" role="group"
aria-labelledby="59d40e705d334deaaebc538ea767c3c7-problem-title"
data-problem-id="block-v1:MITx+24.118x+2T2020+type@problem+block@59d40e705d334deaaebc538ea767c3c7" data-url="/courses/course-v1:MITx+24.118x+2T2020/xblock/block-v1:MITx+24.118x+2T2020+type@problem+block@59d40e705d334deaaebc538ea767c3c7/handler/xmodule_handler"
data-problem-score="0"
data-problem-total-possible="2"
data-attempts-used="0"
data-content="
<h3 class="hd hd-3 problem-header" id="59d40e705d334deaaebc538ea767c3c7-problem-title" aria-describedby="block-v1:MITx+24.118x+2T2020+type@problem+block@59d40e705d334deaaebc538ea767c3c7-problem-progress" tabindex="-1">
Problem 1
</h3>
<div class="problem-progress" id="block-v1:MITx+24.118x+2T2020+type@problem+block@59d40e705d334deaaebc538ea767c3c7-problem-progress"></div>
<div class="problem">
<div>
<p>
<span style="font-family: 'book antiqua', palatino;">Alice and Bob make independent decisions to go for a walk in the park on Tuesday afternoon, and neither of them brings an umbrella. Let <span class="math inline">\(A\)</span> be the event of Alice&#8217;s getting soaked in rain, and <span class="math inline">\(B\)</span> be the event of Bob&#8217;s getting soaked in rain. Are <span class="math inline">\(A\)</span> and <span class="math inline">\(B\)</span> probabilistically independent?</span>
</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div class="choicegroup capa_inputtype" id="inputtype_59d40e705d334deaaebc538ea767c3c7_2_1">
<fieldset aria-describedby="status_59d40e705d334deaaebc538ea767c3c7_2_1">
<div class="field">
<input type="radio" name="input_59d40e705d334deaaebc538ea767c3c7_2_1" id="input_59d40e705d334deaaebc538ea767c3c7_2_1_choice_0" class="field-input input-radio" value="choice_0"/><label id="59d40e705d334deaaebc538ea767c3c7_2_1-choice_0-label" for="input_59d40e705d334deaaebc538ea767c3c7_2_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_59d40e705d334deaaebc538ea767c3c7_2_1">
<span style="font-family: 'book antiqua', palatino;">Yes.</span>
</label>
</div>
<div class="field">
<input type="radio" name="input_59d40e705d334deaaebc538ea767c3c7_2_1" id="input_59d40e705d334deaaebc538ea767c3c7_2_1_choice_1" class="field-input input-radio" value="choice_1"/><label id="59d40e705d334deaaebc538ea767c3c7_2_1-choice_1-label" for="input_59d40e705d334deaaebc538ea767c3c7_2_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_59d40e705d334deaaebc538ea767c3c7_2_1">
<span style="font-family: 'book antiqua', palatino;">No.</span>
</label>
</div>
<span id="answer_59d40e705d334deaaebc538ea767c3c7_2_1"/>
</fieldset>
<div class="indicator-container">
<span class="status unanswered" id="status_59d40e705d334deaaebc538ea767c3c7_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
</div></div>
<p>
<span style="font-family: 'book antiqua', palatino;">Are they causally independent?</span>
</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 2" role="group"><div class="choicegroup capa_inputtype" id="inputtype_59d40e705d334deaaebc538ea767c3c7_3_1">
<fieldset aria-describedby="status_59d40e705d334deaaebc538ea767c3c7_3_1">
<div class="field">
<input type="radio" name="input_59d40e705d334deaaebc538ea767c3c7_3_1" id="input_59d40e705d334deaaebc538ea767c3c7_3_1_choice_0" class="field-input input-radio" value="choice_0"/><label id="59d40e705d334deaaebc538ea767c3c7_3_1-choice_0-label" for="input_59d40e705d334deaaebc538ea767c3c7_3_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_59d40e705d334deaaebc538ea767c3c7_3_1">
<span style="font-family: 'book antiqua', palatino;">Yes.</span>
</label>
</div>
<div class="field">
<input type="radio" name="input_59d40e705d334deaaebc538ea767c3c7_3_1" id="input_59d40e705d334deaaebc538ea767c3c7_3_1_choice_1" class="field-input input-radio" value="choice_1"/><label id="59d40e705d334deaaebc538ea767c3c7_3_1-choice_1-label" for="input_59d40e705d334deaaebc538ea767c3c7_3_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_59d40e705d334deaaebc538ea767c3c7_3_1">
<span style="font-family: 'book antiqua', palatino;">No.</span>
</label>
</div>
<span id="answer_59d40e705d334deaaebc538ea767c3c7_3_1"/>
</fieldset>
<div class="indicator-container">
<span class="status unanswered" id="status_59d40e705d334deaaebc538ea767c3c7_3_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
</div></div>
<div class="solution-span">
<span id="solution_59d40e705d334deaaebc538ea767c3c7_solution_1"/>
</div></div>
<div class="action">
<input type="hidden" name="problem_id" value="Problem 1" />
<div class="submit-attempt-container">
<button type="button" class="submit btn-brand" data-submitting="Submitting" data-value="Submit" data-should-enable-submit-button="True" aria-describedby="submission_feedback_59d40e705d334deaaebc538ea767c3c7" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_59d40e705d334deaaebc538ea767c3c7">
<span class="sr">Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.</span>
</div>
</div>
<div class="problem-action-buttons-wrapper">
</div>
</div>
<div class="notification warning notification-gentle-alert
is-hidden"
tabindex="-1">
<span class="icon fa fa-exclamation-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="59d40e705d334deaaebc538ea767c3c7-problem-title">
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification warning notification-save
is-hidden"
tabindex="-1">
<span class="icon fa fa-save" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="59d40e705d334deaaebc538ea767c3c7-problem-title">None
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification general notification-show-answer
is-hidden"
tabindex="-1">
<span class="icon fa fa-info-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="59d40e705d334deaaebc538ea767c3c7-problem-title">Answers are displayed within the problem
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
</div>
"
data-graded="False">
<p class="loading-spinner">
<i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i>
<span class="sr">Loading…</span>
</p>
</div>
</div>
</div>
<div class="vert vert-2" data-id="block-v1:MITx+24.118x+2T2020+type@problem+block@baec00831f2b443e8349a80a39cd2d2f">
<div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-init="XBlockToXModuleShim" data-has-score="True" data-runtime-version="1" data-graded="False" data-usage-id="block-v1:MITx+24.118x+2T2020+type@problem+block@baec00831f2b443e8349a80a39cd2d2f" data-runtime-class="LmsRuntime" data-block-type="problem" data-request-token="8c3580a8035811efb61a02329aca76dd" data-course-id="course-v1:MITx+24.118x+2T2020">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_baec00831f2b443e8349a80a39cd2d2f" class="problems-wrapper" role="group"
aria-labelledby="baec00831f2b443e8349a80a39cd2d2f-problem-title"
data-problem-id="block-v1:MITx+24.118x+2T2020+type@problem+block@baec00831f2b443e8349a80a39cd2d2f" data-url="/courses/course-v1:MITx+24.118x+2T2020/xblock/block-v1:MITx+24.118x+2T2020+type@problem+block@baec00831f2b443e8349a80a39cd2d2f/handler/xmodule_handler"
data-problem-score="0"
data-problem-total-possible="2"
data-attempts-used="0"
data-content="
<h3 class="hd hd-3 problem-header" id="baec00831f2b443e8349a80a39cd2d2f-problem-title" aria-describedby="block-v1:MITx+24.118x+2T2020+type@problem+block@baec00831f2b443e8349a80a39cd2d2f-problem-progress" tabindex="-1">
Problem 2
</h3>
<div class="problem-progress" id="block-v1:MITx+24.118x+2T2020+type@problem+block@baec00831f2b443e8349a80a39cd2d2f-problem-progress"></div>
<div class="problem">
<div>
<p>
<span style="font-family: 'book antiqua', palatino;">Let <span class="math inline">\(S\)</span> be the event of Jones&#8217;s smoking, and <span class="math inline">\(C\)</span> be the event of Jones&#8217;s being diagnosed with lung cancer. Are <span class="math inline">\(S\)</span> and <span class="math inline">\(C\)</span> probabilistically independent?</span>
</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div class="choicegroup capa_inputtype" id="inputtype_baec00831f2b443e8349a80a39cd2d2f_2_1">
<fieldset aria-describedby="status_baec00831f2b443e8349a80a39cd2d2f_2_1">
<div class="field">
<input type="radio" name="input_baec00831f2b443e8349a80a39cd2d2f_2_1" id="input_baec00831f2b443e8349a80a39cd2d2f_2_1_choice_0" class="field-input input-radio" value="choice_0"/><label id="baec00831f2b443e8349a80a39cd2d2f_2_1-choice_0-label" for="input_baec00831f2b443e8349a80a39cd2d2f_2_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_baec00831f2b443e8349a80a39cd2d2f_2_1">
<span style="font-family: 'book antiqua', palatino;">Yes.</span>
</label>
</div>
<div class="field">
<input type="radio" name="input_baec00831f2b443e8349a80a39cd2d2f_2_1" id="input_baec00831f2b443e8349a80a39cd2d2f_2_1_choice_1" class="field-input input-radio" value="choice_1"/><label id="baec00831f2b443e8349a80a39cd2d2f_2_1-choice_1-label" for="input_baec00831f2b443e8349a80a39cd2d2f_2_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_baec00831f2b443e8349a80a39cd2d2f_2_1">
<span style="font-family: 'book antiqua', palatino;">No.</span>
</label>
</div>
<span id="answer_baec00831f2b443e8349a80a39cd2d2f_2_1"/>
</fieldset>
<div class="indicator-container">
<span class="status unanswered" id="status_baec00831f2b443e8349a80a39cd2d2f_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
</div></div>
<p>
<span style="font-family: 'book antiqua', palatino;">Are they causally independent?</span>
</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 2" role="group"><div class="choicegroup capa_inputtype" id="inputtype_baec00831f2b443e8349a80a39cd2d2f_3_1">
<fieldset aria-describedby="status_baec00831f2b443e8349a80a39cd2d2f_3_1">
<div class="field">
<input type="radio" name="input_baec00831f2b443e8349a80a39cd2d2f_3_1" id="input_baec00831f2b443e8349a80a39cd2d2f_3_1_choice_0" class="field-input input-radio" value="choice_0"/><label id="baec00831f2b443e8349a80a39cd2d2f_3_1-choice_0-label" for="input_baec00831f2b443e8349a80a39cd2d2f_3_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_baec00831f2b443e8349a80a39cd2d2f_3_1">
<span style="font-family: 'book antiqua', palatino;">Yes.</span>
</label>
</div>
<div class="field">
<input type="radio" name="input_baec00831f2b443e8349a80a39cd2d2f_3_1" id="input_baec00831f2b443e8349a80a39cd2d2f_3_1_choice_1" class="field-input input-radio" value="choice_1"/><label id="baec00831f2b443e8349a80a39cd2d2f_3_1-choice_1-label" for="input_baec00831f2b443e8349a80a39cd2d2f_3_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_baec00831f2b443e8349a80a39cd2d2f_3_1">
<span style="font-family: 'book antiqua', palatino;">No.</span>
</label>
</div>
<span id="answer_baec00831f2b443e8349a80a39cd2d2f_3_1"/>
</fieldset>
<div class="indicator-container">
<span class="status unanswered" id="status_baec00831f2b443e8349a80a39cd2d2f_3_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
</div></div>
<div class="solution-span">
<span id="solution_baec00831f2b443e8349a80a39cd2d2f_solution_1"/>
</div></div>
<div class="action">
<input type="hidden" name="problem_id" value="Problem 2" />
<div class="submit-attempt-container">
<button type="button" class="submit btn-brand" data-submitting="Submitting" data-value="Submit" data-should-enable-submit-button="True" aria-describedby="submission_feedback_baec00831f2b443e8349a80a39cd2d2f" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_baec00831f2b443e8349a80a39cd2d2f">
<span class="sr">Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.</span>
</div>
</div>
<div class="problem-action-buttons-wrapper">
</div>
</div>
<div class="notification warning notification-gentle-alert
is-hidden"
tabindex="-1">
<span class="icon fa fa-exclamation-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="baec00831f2b443e8349a80a39cd2d2f-problem-title">
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification warning notification-save
is-hidden"
tabindex="-1">
<span class="icon fa fa-save" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="baec00831f2b443e8349a80a39cd2d2f-problem-title">None
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification general notification-show-answer
is-hidden"
tabindex="-1">
<span class="icon fa fa-info-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="baec00831f2b443e8349a80a39cd2d2f-problem-title">Answers are displayed within the problem
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
</div>
"
data-graded="False">
<p class="loading-spinner">
<i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i>
<span class="sr">Loading…</span>
</p>
</div>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-init="VerticalStudentView" data-has-score="False" data-runtime-version="1" data-graded="False" data-usage-id="block-v1:MITx+24.118x+2T2020+type@vertical+block@517cc8cb955d4989b91fdc470fdfb3fe" data-runtime-class="LmsRuntime" data-block-type="vertical" data-request-token="8c3580a8035811efb61a02329aca76dd" data-course-id="course-v1:MITx+24.118x+2T2020">
<h2 class="hd hd-2 unit-title">Two Types of Conditionals</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+24.118x+2T2020+type@html+block@0e136bbbd1c54f1abf662b517daeb99f">
<div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-init="XBlockToXModuleShim" data-has-score="False" data-runtime-version="1" data-graded="False" data-usage-id="block-v1:MITx+24.118x+2T2020+type@html+block@0e136bbbd1c54f1abf662b517daeb99f" data-runtime-class="LmsRuntime" data-block-type="html" data-request-token="8c3580a8035811efb61a02329aca76dd" data-course-id="course-v1:MITx+24.118x+2T2020">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "HTMLModule"}
</script>
<p><span style="font-family: book antiqua, palatino;">Like many other natural languages, English has a nice way of tracking the distinction between probabilistic and causal dependence. </span><br /><br /><span style="font-family: book antiqua, palatino;"><strong>Indicative conditionals</strong> are conditionals of the form <em>if A, then B</em>, and they track probabilistic dependence. More specifically: the probability of <em>if A, then B</em> is always the probability of <em>B</em> conditional on <em>A</em>. Consider, for example, the indicative conditional:</span></p>
<p style="padding-left: 30px;"><span style="font-family: book antiqua, palatino;">If people are using their umbrellas, it's raining.</span></p>
<p><span style="font-family: book antiqua, palatino;">The probability of rain conditional on people using their umbrellas is high. So we should be fairly confident that this conditional is true.</span><br /><br /><span style="font-family: book antiqua, palatino;"><strong>Subjunctive conditionals</strong> are conditionals of the form <em>if it were that A, it would be that B</em>. Unlike indicative conditionals, subjunctive conditionals do not track probabilistic dependence. To see this, suppose that it's sunny outside. Then, unlike its indicative counterpart, the following subjunctive conditional is false:</span></p>
<p style="padding-left: 30px;"><span style="font-family: book antiqua, palatino;">If people were to use their umbrellas, there would be rain.</span></p>
<p><span style="font-family: book antiqua, palatino;">For if it's sunny outside and people to start opening their umbrellas, it will remain just as sunny.</span><br /><br /><span style="font-family: book antiqua, palatino;">Subjunctive conditionals are interesting because they track an important aspect of causal dependence. Simplifying a bit: if <em>A</em> causes <em>B</em>, then the subjunctive conditional "if it were that <em>A</em>, it would be that <em>B</em>'' is true. For example, the fact that rain causes umbrella use means that the following subjunctive conditional is true:</span></p>
<p style="padding-left: 30px;"><span style="font-family: book antiqua, palatino;">If it were to rain, people would use their umbrellas.</span></p>
<p><span style="font-family: book antiqua, palatino;">Subjunctive conditionals can also be used to keep track of causal independence. For example, one can capture the fact that umbrella use has no causal effect on rain by noting that the following subjunctive conditionals are both true, assuming it's sunny outside:</span></p>
<p style="padding-left: 30px;"><span style="font-family: book antiqua, palatino;">If people were to use their umbrellas, it would (still) be sunny outside.</span><br /><span style="font-family: book antiqua, palatino;">If people were to refrain from using their umbrellas, it would (still) be sunny outside.</span></p>
<p><span style="font-family: book antiqua, palatino;">(Although I have tried to keep things relatively simple for the purposes of the present discussion, conditionals are fairly perplexing. My MIT colleague <a href="http://web.mit.edu/jkhoo/www/" target="[object Object]">Justin Khoo</a> gives an excellent introduction to the weird world of conditionals in <a href="https://www.youtube.com/watch?v=4Zxp2-_pLCE" target="[object Object]">this series of WiPhi videos</a>.)</span></p>
<p></p>
<p></p>
</div>
</div>
<div class="vert vert-1" data-id="block-v1:MITx+24.118x+2T2020+type@problem+block@c2aba72148c944d7b21bdcbc49208cf7">
<div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-init="XBlockToXModuleShim" data-has-score="True" data-runtime-version="1" data-graded="False" data-usage-id="block-v1:MITx+24.118x+2T2020+type@problem+block@c2aba72148c944d7b21bdcbc49208cf7" data-runtime-class="LmsRuntime" data-block-type="problem" data-request-token="8c3580a8035811efb61a02329aca76dd" data-course-id="course-v1:MITx+24.118x+2T2020">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_c2aba72148c944d7b21bdcbc49208cf7" class="problems-wrapper" role="group"
aria-labelledby="c2aba72148c944d7b21bdcbc49208cf7-problem-title"
data-problem-id="block-v1:MITx+24.118x+2T2020+type@problem+block@c2aba72148c944d7b21bdcbc49208cf7" data-url="/courses/course-v1:MITx+24.118x+2T2020/xblock/block-v1:MITx+24.118x+2T2020+type@problem+block@c2aba72148c944d7b21bdcbc49208cf7/handler/xmodule_handler"
data-problem-score="0"
data-problem-total-possible="1"
data-attempts-used="0"
data-content="
<h3 class="hd hd-3 problem-header" id="c2aba72148c944d7b21bdcbc49208cf7-problem-title" aria-describedby="block-v1:MITx+24.118x+2T2020+type@problem+block@c2aba72148c944d7b21bdcbc49208cf7-problem-progress" tabindex="-1">
Problem 1
</h3>
<div class="problem-progress" id="block-v1:MITx+24.118x+2T2020+type@problem+block@c2aba72148c944d7b21bdcbc49208cf7-problem-progress"></div>
<div class="problem">
<div>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><p>
<span style="font-family: 'book antiqua', palatino;">Here is a famous pair of conditionals, due to philosopher Ernest Adams:</span>
</p>
<span style="font-family: 'book antiqua', palatino;">
<blockquote>
<p>
<span style="font-family: 'book antiqua', palatino;">[Didn&#8217;t]<br/>
If Oswald didn&#8217;t kill Kennedy, somebody else did.</span>
</p>
</blockquote>
</span>
<span style="font-family: 'book antiqua', palatino;">
<blockquote>
<p>
<span style="font-family: 'book antiqua', palatino;">[Hadn&#8217;t]<br/>
If Oswald hadn&#8217;t killed Kennedy, somebody else would have.</span>
</p>
</blockquote>
</span>
<p>
<span style="font-family: 'book antiqua', palatino;">Do these conditionals differ in truth value? (In thinking about your answer, assume that Kennedy was shot, but that there was no conspiracy: Oswald acted alone.)</span>
</p>
<div class="choicegroup capa_inputtype" id="inputtype_c2aba72148c944d7b21bdcbc49208cf7_2_1">
<fieldset aria-describedby="status_c2aba72148c944d7b21bdcbc49208cf7_2_1">
<div class="field">
<input type="radio" name="input_c2aba72148c944d7b21bdcbc49208cf7_2_1" id="input_c2aba72148c944d7b21bdcbc49208cf7_2_1_choice_0" class="field-input input-radio" value="choice_0"/><label id="c2aba72148c944d7b21bdcbc49208cf7_2_1-choice_0-label" for="input_c2aba72148c944d7b21bdcbc49208cf7_2_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_c2aba72148c944d7b21bdcbc49208cf7_2_1">
<span style="font-family: 'book antiqua', palatino;">Yes, they differ in truth value.</span>
</label>
</div>
<div class="field">
<input type="radio" name="input_c2aba72148c944d7b21bdcbc49208cf7_2_1" id="input_c2aba72148c944d7b21bdcbc49208cf7_2_1_choice_1" class="field-input input-radio" value="choice_1"/><label id="c2aba72148c944d7b21bdcbc49208cf7_2_1-choice_1-label" for="input_c2aba72148c944d7b21bdcbc49208cf7_2_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_c2aba72148c944d7b21bdcbc49208cf7_2_1">
<span style="font-family: 'book antiqua', palatino;">No, they don't.</span>
</label>
</div>
<span id="answer_c2aba72148c944d7b21bdcbc49208cf7_2_1"/>
</fieldset>
<div class="indicator-container">
<span class="status unanswered" id="status_c2aba72148c944d7b21bdcbc49208cf7_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
</div><div class="solution-span">
<span id="solution_c2aba72148c944d7b21bdcbc49208cf7_solution_1"/>
</div></div>
</div>
<div class="action">
<input type="hidden" name="problem_id" value="Problem 1" />
<div class="submit-attempt-container">
<button type="button" class="submit btn-brand" data-submitting="Submitting" data-value="Submit" data-should-enable-submit-button="True" aria-describedby="submission_feedback_c2aba72148c944d7b21bdcbc49208cf7" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_c2aba72148c944d7b21bdcbc49208cf7">
<span class="sr">Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.</span>
</div>
</div>
<div class="problem-action-buttons-wrapper">
</div>
</div>
<div class="notification warning notification-gentle-alert
is-hidden"
tabindex="-1">
<span class="icon fa fa-exclamation-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="c2aba72148c944d7b21bdcbc49208cf7-problem-title">
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification warning notification-save
is-hidden"
tabindex="-1">
<span class="icon fa fa-save" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="c2aba72148c944d7b21bdcbc49208cf7-problem-title">None
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification general notification-show-answer
is-hidden"
tabindex="-1">
<span class="icon fa fa-info-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="c2aba72148c944d7b21bdcbc49208cf7-problem-title">Answers are displayed within the problem
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
</div>
"
data-graded="False">
<p class="loading-spinner">
<i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i>
<span class="sr">Loading…</span>
</p>
</div>
</div>
</div>
<div class="vert vert-2" data-id="block-v1:MITx+24.118x+2T2020+type@problem+block@85c5ee68d760493383b6c939ce70b27e">
<div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-init="XBlockToXModuleShim" data-has-score="True" data-runtime-version="1" data-graded="False" data-usage-id="block-v1:MITx+24.118x+2T2020+type@problem+block@85c5ee68d760493383b6c939ce70b27e" data-runtime-class="LmsRuntime" data-block-type="problem" data-request-token="8c3580a8035811efb61a02329aca76dd" data-course-id="course-v1:MITx+24.118x+2T2020">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_85c5ee68d760493383b6c939ce70b27e" class="problems-wrapper" role="group"
aria-labelledby="85c5ee68d760493383b6c939ce70b27e-problem-title"
data-problem-id="block-v1:MITx+24.118x+2T2020+type@problem+block@85c5ee68d760493383b6c939ce70b27e" data-url="/courses/course-v1:MITx+24.118x+2T2020/xblock/block-v1:MITx+24.118x+2T2020+type@problem+block@85c5ee68d760493383b6c939ce70b27e/handler/xmodule_handler"
data-problem-score="0"
data-problem-total-possible="1"
data-attempts-used="0"
data-content="
<h3 class="hd hd-3 problem-header" id="85c5ee68d760493383b6c939ce70b27e-problem-title" aria-describedby="block-v1:MITx+24.118x+2T2020+type@problem+block@85c5ee68d760493383b6c939ce70b27e-problem-progress" tabindex="-1">
Problem 2
</h3>
<div class="problem-progress" id="block-v1:MITx+24.118x+2T2020+type@problem+block@85c5ee68d760493383b6c939ce70b27e-problem-progress"></div>
<div class="problem">
<div>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><p>
<span style="font-family: 'book antiqua', palatino;">Recall the <a href="/courses/course-v1:MITx+24.118x+2T2020/jump_to_id/9ffa2d7c495f4f87a3a8f8deaa765fc8">&#8220;Death in Damascus&#8221; story</a> from Lecture 4. Imagine the merchant&#8217;s situation just after Death has warned her that they will meet tomorrow, and suppose she says to herself &#8220;If I stay in Damascus, Death will meet me in Damascus&#8221;.</span>
</p>
<p>
<span style="font-family: 'book antiqua', palatino;">Is this indicative conditional true? (Assume that Death is completely reliable.)</span>
</p>
<div class="choicegroup capa_inputtype" id="inputtype_85c5ee68d760493383b6c939ce70b27e_2_1">
<fieldset aria-describedby="status_85c5ee68d760493383b6c939ce70b27e_2_1">
<div class="field">
<input type="radio" name="input_85c5ee68d760493383b6c939ce70b27e_2_1" id="input_85c5ee68d760493383b6c939ce70b27e_2_1_choice_0" class="field-input input-radio" value="choice_0"/><label id="85c5ee68d760493383b6c939ce70b27e_2_1-choice_0-label" for="input_85c5ee68d760493383b6c939ce70b27e_2_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_85c5ee68d760493383b6c939ce70b27e_2_1">
<span style="font-family: 'book antiqua', palatino;">Yes, it's true.</span>
</label>
</div>
<div class="field">
<input type="radio" name="input_85c5ee68d760493383b6c939ce70b27e_2_1" id="input_85c5ee68d760493383b6c939ce70b27e_2_1_choice_1" class="field-input input-radio" value="choice_1"/><label id="85c5ee68d760493383b6c939ce70b27e_2_1-choice_1-label" for="input_85c5ee68d760493383b6c939ce70b27e_2_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_85c5ee68d760493383b6c939ce70b27e_2_1">
<span style="font-family: 'book antiqua', palatino;">No, it isn't.</span>
</label>
</div>
<span id="answer_85c5ee68d760493383b6c939ce70b27e_2_1"/>
</fieldset>
<div class="indicator-container">
<span class="status unanswered" id="status_85c5ee68d760493383b6c939ce70b27e_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
</div><div class="solution-span">
<span id="solution_85c5ee68d760493383b6c939ce70b27e_solution_1"/>
</div></div>
</div>
<div class="action">
<input type="hidden" name="problem_id" value="Problem 2" />
<div class="submit-attempt-container">
<button type="button" class="submit btn-brand" data-submitting="Submitting" data-value="Submit" data-should-enable-submit-button="True" aria-describedby="submission_feedback_85c5ee68d760493383b6c939ce70b27e" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_85c5ee68d760493383b6c939ce70b27e">
<span class="sr">Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.</span>
</div>
</div>
<div class="problem-action-buttons-wrapper">
</div>
</div>
<div class="notification warning notification-gentle-alert
is-hidden"
tabindex="-1">
<span class="icon fa fa-exclamation-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="85c5ee68d760493383b6c939ce70b27e-problem-title">
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification warning notification-save
is-hidden"
tabindex="-1">
<span class="icon fa fa-save" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="85c5ee68d760493383b6c939ce70b27e-problem-title">None
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification general notification-show-answer
is-hidden"
tabindex="-1">
<span class="icon fa fa-info-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="85c5ee68d760493383b6c939ce70b27e-problem-title">Answers are displayed within the problem
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
</div>
"
data-graded="False">
<p class="loading-spinner">
<i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i>
<span class="sr">Loading…</span>
</p>
</div>
</div>
</div>
<div class="vert vert-3" data-id="block-v1:MITx+24.118x+2T2020+type@problem+block@28a0b673dc2440948aafebcdc037a24e">
<div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-init="XBlockToXModuleShim" data-has-score="True" data-runtime-version="1" data-graded="False" data-usage-id="block-v1:MITx+24.118x+2T2020+type@problem+block@28a0b673dc2440948aafebcdc037a24e" data-runtime-class="LmsRuntime" data-block-type="problem" data-request-token="8c3580a8035811efb61a02329aca76dd" data-course-id="course-v1:MITx+24.118x+2T2020">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_28a0b673dc2440948aafebcdc037a24e" class="problems-wrapper" role="group"
aria-labelledby="28a0b673dc2440948aafebcdc037a24e-problem-title"
data-problem-id="block-v1:MITx+24.118x+2T2020+type@problem+block@28a0b673dc2440948aafebcdc037a24e" data-url="/courses/course-v1:MITx+24.118x+2T2020/xblock/block-v1:MITx+24.118x+2T2020+type@problem+block@28a0b673dc2440948aafebcdc037a24e/handler/xmodule_handler"
data-problem-score="0"
data-problem-total-possible="1"
data-attempts-used="0"
data-content="
<h3 class="hd hd-3 problem-header" id="28a0b673dc2440948aafebcdc037a24e-problem-title" aria-describedby="block-v1:MITx+24.118x+2T2020+type@problem+block@28a0b673dc2440948aafebcdc037a24e-problem-progress" tabindex="-1">
Problem 3
</h3>
<div class="problem-progress" id="block-v1:MITx+24.118x+2T2020+type@problem+block@28a0b673dc2440948aafebcdc037a24e-problem-progress"></div>
<div class="problem">
<div>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><p>
<span style="font-family: 'book antiqua', palatino;">Now consider the merchant&#8217;s situation after she wakes up to find Death in Aleppo, and suppose she says to herself &#8220;Had I stayed in Damascus, Death would have met me in Damascus&#8221;.</span>
</p>
<p>
<span style="font-family: 'book antiqua', palatino;">Is this counterfactual conditional definitely true?</span>
</p>
<div class="choicegroup capa_inputtype" id="inputtype_28a0b673dc2440948aafebcdc037a24e_2_1">
<fieldset aria-describedby="status_28a0b673dc2440948aafebcdc037a24e_2_1">
<div class="field">
<input type="radio" name="input_28a0b673dc2440948aafebcdc037a24e_2_1" id="input_28a0b673dc2440948aafebcdc037a24e_2_1_choice_0" class="field-input input-radio" value="choice_0"/><label id="28a0b673dc2440948aafebcdc037a24e_2_1-choice_0-label" for="input_28a0b673dc2440948aafebcdc037a24e_2_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_28a0b673dc2440948aafebcdc037a24e_2_1">
<span style="font-family: 'book antiqua', palatino;">Yes, it's true.</span>
</label>
</div>
<div class="field">
<input type="radio" name="input_28a0b673dc2440948aafebcdc037a24e_2_1" id="input_28a0b673dc2440948aafebcdc037a24e_2_1_choice_1" class="field-input input-radio" value="choice_1"/><label id="28a0b673dc2440948aafebcdc037a24e_2_1-choice_1-label" for="input_28a0b673dc2440948aafebcdc037a24e_2_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_28a0b673dc2440948aafebcdc037a24e_2_1">
<span style="font-family: 'book antiqua', palatino;">No, it isn't.</span>
</label>
</div>
<span id="answer_28a0b673dc2440948aafebcdc037a24e_2_1"/>
</fieldset>
<div class="indicator-container">
<span class="status unanswered" id="status_28a0b673dc2440948aafebcdc037a24e_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
</div><div class="solution-span">
<span id="solution_28a0b673dc2440948aafebcdc037a24e_solution_1"/>
</div></div>
</div>
<div class="action">
<input type="hidden" name="problem_id" value="Problem 3" />
<div class="submit-attempt-container">
<button type="button" class="submit btn-brand" data-submitting="Submitting" data-value="Submit" data-should-enable-submit-button="True" aria-describedby="submission_feedback_28a0b673dc2440948aafebcdc037a24e" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_28a0b673dc2440948aafebcdc037a24e">
<span class="sr">Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.</span>
</div>
</div>
<div class="problem-action-buttons-wrapper">
</div>
</div>
<div class="notification warning notification-gentle-alert
is-hidden"
tabindex="-1">
<span class="icon fa fa-exclamation-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="28a0b673dc2440948aafebcdc037a24e-problem-title">
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification warning notification-save
is-hidden"
tabindex="-1">
<span class="icon fa fa-save" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="28a0b673dc2440948aafebcdc037a24e-problem-title">None
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification general notification-show-answer
is-hidden"
tabindex="-1">
<span class="icon fa fa-info-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="28a0b673dc2440948aafebcdc037a24e-problem-title">Answers are displayed within the problem
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
</div>
"
data-graded="False">
<p class="loading-spinner">
<i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i>
<span class="sr">Loading…</span>
</p>
</div>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-init="VerticalStudentView" data-has-score="False" data-runtime-version="1" data-graded="False" data-usage-id="block-v1:MITx+24.118x+2T2020+type@vertical+block@119e939c80c34038a65d3de1a40cb6ca" data-runtime-class="LmsRuntime" data-block-type="vertical" data-request-token="8c3580a8035811efb61a02329aca76dd" data-course-id="course-v1:MITx+24.118x+2T2020">
<h2 class="hd hd-2 unit-title">An Alternate Characterization of Expected Value</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+24.118x+2T2020+type@html+block@c8ca930db25b4ecc8174af0ffa9401e8">
<div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-init="XBlockToXModuleShim" data-has-score="False" data-runtime-version="1" data-graded="False" data-usage-id="block-v1:MITx+24.118x+2T2020+type@html+block@c8ca930db25b4ecc8174af0ffa9401e8" data-runtime-class="LmsRuntime" data-block-type="html" data-request-token="8c3580a8035811efb61a02329aca76dd" data-course-id="course-v1:MITx+24.118x+2T2020">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "HTMLModule"}
</script>
<p><span style="font-family: book antiqua, palatino;">Causal Decision Theory is a variant of decision theory that is based on Expected Value Maximization but uses an alternate definition of expected value. It holds onto the idea that expected value of an option is a weighted average of the values of the different outcomes that the option might lead to, but does the weighting differently. </span><br /><br /><span style="font-family: book antiqua, palatino;">The characterization of expected value we have been discussing so far is sometimes called Evidential Decision Theory. As we have seen, it uses <em>probabilistic dependence</em> to determine how much weight to give each of the possible outcomes of one's actions. More specifically, it weighs an outcome using the <em>conditional probability</em> of the outcome given the relevant action.</span><br /><br /><span style="font-family: book antiqua, palatino;">Let us review how this plays out in a Newcomb scenario. In calculating the expected value of one-boxing, one weighs an outcome in which you one-box (\(1\!B\)) and the large box is full \((F)\) using \(p(F|1\!B)\), and one weighs an outcome in which you one-box and the large box is empty \((E)\) using \(p(E|1\!B)\). And similarly when one calculates the expected value of two-boxing \((2\!B)\). This yields the following familiar results:<br /></span>\[ \begin{array}{ccc} EV(1\!B) &= &v(1\!B\, F) \cdot p(F|1\!B) + v(1\!B\,E) \cdot p(E|1\!B)\\ EV(2\!B) &= &v(2\!B\, F) \cdot p(F|2\!B) + v(2\!B\,E) \cdot p(E|2\!B)\\ \end{array} \] <span style="font-family: book antiqua, palatino;">Because the probability of an indicative conditional is the probability of the conditional's consequent given its antecedent, these equations could also be written as follows, where "\(A \rightarrow B\)'' is the indicative conditional "if \(A\), then \(B\)'':</span><br />\[ \begin{array}{ccc} EV(1\!B) &= &v(1\!B\, F) \cdot p(1\!B \rightarrow F) + v(1\!B\,E) \cdot p(1\!B\rightarrow E)\\ EV(2\!B) &= &v(2\!B\, F) \cdot p(2\!B \rightarrow F) + v(2\!B\,E) \cdot p(2\!B \rightarrow E)\\ \end{array} \] <span style="font-family: book antiqua, palatino;">On either version of the equations, Expected Value Maximization delivers the conclusion that one ought to one-box.</span></p>
<p><span style="font-family: book antiqua, palatino;">Causal decision theorists see things differently. They think that one should use <em>causal dependence</em> to determine how much weight to give each of the possible outcomes of one's actions. More specifically, they think that one should weigh an outcome not by using the probability of an indicative conditional, but by using the probability of the corresponding <em>subjunctive</em> conditional; specifically the subjunctive conditional <em>were you to perform the relevant action, the outcome would come about</em>. </span><br /><br /><span style="font-family: book antiqua, palatino;">Suppose, for example, that one wishes to calculate the expected value of one-boxing. How should one weigh an outcome in which you one-box and the large box is full? According to causal decision theory, you should use the probability of the following subjunctive conditional: <em>were you to one-box, a full-box outcome would come about</em>. In symbols:</span><br /><span style="font-family: book antiqua, palatino;">\[ \begin{array}{ccc} EV(1\!B) &= &v(1\!B\, F) \cdot p(1\!B \, \Box \!\! \rightarrow F) + v(1\!B\,E) \cdot p(1\!B \,\Box \!\! \rightarrow E)\\ \end{array} \] And similarly for two-boxing:<br /></span><span style="font-family: book antiqua, palatino;">\[ \begin{array}{ccc} EV(2\!B) &= &v(2\!B\, F) \cdot p(2\!B \,\Box \!\! \rightarrow F) + v(2\!B\,E) \cdot p(2\!B \, \Box \!\! \rightarrow E)\\ \end{array} \] Notice that these are exactly like the equations endorsed by the evidential decision theorists, except that we use subjunctive conditionals instead of indicative conditionals.</span><br /><br /><span style="font-family: book antiqua, palatino;">As it turns out, the causal decision theorist's equations can be simplified a bit in the present case. For recall that you have no control over the contents of the large box. So under what circumstances will be the case that were you to one box, you would find a full large box? Exactly when the large box is full to begin with. In other words: \(p(1\!B \, \Box \!\! \rightarrow F) = p(F)\). (And similarly for other cases.) So the equations above reduce to:</span><br />\[ \begin{array}{ccc} EV(1\!B) &= &v(1\!B\, F) \cdot p(F) + v(1\!B\,E) \cdot p(E)\\ EV(2\!B) &= &v(2\!B\, F) \cdot p(F) + v(2\!B\,E) \cdot p(E)\\ \end{array} \] <span style="font-family: book antiqua, palatino;">Since the payoff structure of a Newcomb situation guarantees that \(v(2\!B\, F) > v(1\!B\, F)\) and \(v(2\!B\, E) > v(1\!B\, E)\), our equations guarantee that the expected value of two-boxing will be higher than the expected value of one-boxing regardless of the values of \(p(F)\) and \(p(E)\). So causal decision theory vindicates the idea that the rational thing to do in a Newcomb scenario is two-box.</span><br /><br /><span style="font-family: book antiqua, palatino;">As the Newcomb case makes clear, causal decision theory can come apart from evidential decision theory when causal and probabilistic dependence come apart. But they always deliver the same results in cases where causal and probabilistic dependence don't come apart.</span></p>
</div>
</div>
<div class="vert vert-1" data-id="block-v1:MITx+24.118x+2T2020+type@problem+block@8a2a32b8a4a64d929e927bb50c1f0b70">
<div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-init="XBlockToXModuleShim" data-has-score="True" data-runtime-version="1" data-graded="False" data-usage-id="block-v1:MITx+24.118x+2T2020+type@problem+block@8a2a32b8a4a64d929e927bb50c1f0b70" data-runtime-class="LmsRuntime" data-block-type="problem" data-request-token="8c3580a8035811efb61a02329aca76dd" data-course-id="course-v1:MITx+24.118x+2T2020">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_8a2a32b8a4a64d929e927bb50c1f0b70" class="problems-wrapper" role="group"
aria-labelledby="8a2a32b8a4a64d929e927bb50c1f0b70-problem-title"
data-problem-id="block-v1:MITx+24.118x+2T2020+type@problem+block@8a2a32b8a4a64d929e927bb50c1f0b70" data-url="/courses/course-v1:MITx+24.118x+2T2020/xblock/block-v1:MITx+24.118x+2T2020+type@problem+block@8a2a32b8a4a64d929e927bb50c1f0b70/handler/xmodule_handler"
data-problem-score="0"
data-problem-total-possible="1"
data-attempts-used="0"
data-content="
<h3 class="hd hd-3 problem-header" id="8a2a32b8a4a64d929e927bb50c1f0b70-problem-title" aria-describedby="block-v1:MITx+24.118x+2T2020+type@problem+block@8a2a32b8a4a64d929e927bb50c1f0b70-problem-progress" tabindex="-1">
Problem 1
</h3>
<div class="problem-progress" id="block-v1:MITx+24.118x+2T2020+type@problem+block@8a2a32b8a4a64d929e927bb50c1f0b70-problem-progress"></div>
<div class="problem">
<div>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div class="choicegroup capa_inputtype" id="inputtype_8a2a32b8a4a64d929e927bb50c1f0b70_2_1">
<fieldset aria-describedby="status_8a2a32b8a4a64d929e927bb50c1f0b70_2_1">
<legend id="8a2a32b8a4a64d929e927bb50c1f0b70_2_1-legend" class="response-fieldset-legend field-group-hd"><span style="font-family: 'book antiqua', palatino;">Consider a variant of the Newcomb scenario in which the predictor decides whether to fill the large box by flipping a coin. Do Causal and Evidential Decision Theory deliver different results?</span></legend>
<div class="field">
<input type="radio" name="input_8a2a32b8a4a64d929e927bb50c1f0b70_2_1" id="input_8a2a32b8a4a64d929e927bb50c1f0b70_2_1_choice_0" class="field-input input-radio" value="choice_0"/><label id="8a2a32b8a4a64d929e927bb50c1f0b70_2_1-choice_0-label" for="input_8a2a32b8a4a64d929e927bb50c1f0b70_2_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_8a2a32b8a4a64d929e927bb50c1f0b70_2_1"> <span style="font-family: 'book antiqua', palatino;">Yes, they deliver different results</span>.
</label>
</div>
<div class="field">
<input type="radio" name="input_8a2a32b8a4a64d929e927bb50c1f0b70_2_1" id="input_8a2a32b8a4a64d929e927bb50c1f0b70_2_1_choice_1" class="field-input input-radio" value="choice_1"/><label id="8a2a32b8a4a64d929e927bb50c1f0b70_2_1-choice_1-label" for="input_8a2a32b8a4a64d929e927bb50c1f0b70_2_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_8a2a32b8a4a64d929e927bb50c1f0b70_2_1"> <span style="font-family: 'book antiqua', palatino;">No, they deliver the same result</span>.
</label>
</div>
<span id="answer_8a2a32b8a4a64d929e927bb50c1f0b70_2_1"/>
</fieldset>
<div class="indicator-container">
<span class="status unanswered" id="status_8a2a32b8a4a64d929e927bb50c1f0b70_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
</div><div class="solution-span">
<span id="solution_8a2a32b8a4a64d929e927bb50c1f0b70_solution_1"/>
</div></div>
</div>
<div class="action">
<input type="hidden" name="problem_id" value="Problem 1" />
<div class="submit-attempt-container">
<button type="button" class="submit btn-brand" data-submitting="Submitting" data-value="Submit" data-should-enable-submit-button="True" aria-describedby="submission_feedback_8a2a32b8a4a64d929e927bb50c1f0b70" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_8a2a32b8a4a64d929e927bb50c1f0b70">
<span class="sr">Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.</span>
</div>
</div>
<div class="problem-action-buttons-wrapper">
</div>
</div>
<div class="notification warning notification-gentle-alert
is-hidden"
tabindex="-1">
<span class="icon fa fa-exclamation-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="8a2a32b8a4a64d929e927bb50c1f0b70-problem-title">
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification warning notification-save
is-hidden"
tabindex="-1">
<span class="icon fa fa-save" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="8a2a32b8a4a64d929e927bb50c1f0b70-problem-title">None
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification general notification-show-answer
is-hidden"
tabindex="-1">
<span class="icon fa fa-info-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="8a2a32b8a4a64d929e927bb50c1f0b70-problem-title">Answers are displayed within the problem
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
</div>
"
data-graded="False">
<p class="loading-spinner">
<i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i>
<span class="sr">Loading…</span>
</p>
</div>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-init="VerticalStudentView" data-has-score="False" data-runtime-version="1" data-graded="False" data-usage-id="block-v1:MITx+24.118x+2T2020+type@vertical+block@860fa20608ad46d49e6bfa7103c191e4" data-runtime-class="LmsRuntime" data-block-type="vertical" data-request-token="8c3580a8035811efb61a02329aca76dd" data-course-id="course-v1:MITx+24.118x+2T2020">
<h2 class="hd hd-2 unit-title">A Connection to Free Will</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+24.118x+2T2020+type@html+block@28f3e4cf6d044b218a876b7dbf6fb29a">
<div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-init="XBlockToXModuleShim" data-has-score="False" data-runtime-version="1" data-graded="False" data-usage-id="block-v1:MITx+24.118x+2T2020+type@html+block@28f3e4cf6d044b218a876b7dbf6fb29a" data-runtime-class="LmsRuntime" data-block-type="html" data-request-token="8c3580a8035811efb61a02329aca76dd" data-course-id="course-v1:MITx+24.118x+2T2020">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "HTMLModule"}
</script>
<p><span style="font-family: 'book antiqua', palatino;">There is an interesting connection between causal decision theory and some of the ideas we discussed in Chapter 4, when we talked about free will. Recall your friend Susan. You are having breakfast with her in New York, and she tells you that last night she was thinking of taking a train trip to Alaska. This puts you in a position to know that the following indicative conditional is true:</span></p>
<p style="padding-left: 30px;"><span style="font-family: 'book antiqua', palatino;">If Susan decided to make a train trip to Alaska last night, she failed to do so.</span></p>
<p><span style="font-family: 'book antiqua', palatino;">The reason is that you can see that Susan is in New York the next morning, and know that a train trip to from New York to Alaska cannot be completed in a single night. In contrast, it is not clear whether you should think that the following subjunctive conditional was true at a time in which Susan was still deciding what to do:</span></p>
<p style="padding-left: 30px;"><span style="font-family: 'book antiqua', palatino;">Were Susan to decide to make the trip to Alaska, she would succeed in bringing about the trip.</span></p>
<p><span style="font-family: 'book antiqua', palatino;">If all trains out of New York were cancelled last night because of a storm, this conditional is false. But if a suitable train left New York last night, and if there was nothing to stop Susan from taking it had she decided to do so, the conditional is true.</span></p>
<p><span style="font-family: book antiqua, palatino;">Recall that our discussion of free will in Lecture 4 focused on the Control Hypothesis: the hypothesis that to act freely is to be in a position to do otherwise. According to the Control Hypothesis, the truth of the indicative conditional above is irrelevant to the question of whether Susan acted freely in staying in New York. But the subjunctive conditional is extremely relevant. For the Control Hypothesis sees acting freely as a matter of being in a position to <em>cause</em> a different outcome, and it is the subjunctive conditional, rather than its indicative counterpart, that tracks causal dependence. </span></p>
<p><span style="font-family: 'book antiqua', palatino;">Something similar is true of causal decision theory. Notice, in particular, that the causal decision theorist agrees that the following two indicative conditionals are both true of a Newcomb scenario.</span></p>
<p style="padding-left: 30px;"><span style="font-family: 'book antiqua', palatino;">If you one-box, you’ll almost certainly be rich.<br />If you two-box, you’ll almost certainly be poor.</span></p>
<p><span style="font-family: 'book antiqua', palatino;">She thinks, however, that their truth is irrelevant to the question of whether one should one-box or two-box. What matters is the fact that the following subjunctive conditionals are both true:</span></p>
<p style="padding-left: 30px;"><span style="font-family: 'book antiqua', palatino;">Were you to one-box, you would fail to bring about a situation in which you end up with as much money as is presently available to you.<br />Were you to two-box, you would succeed in bring about a situation in which you end up with as much money as is presently available to you.</span></p>
<p><span style="font-family: book antiqua, palatino;">This is because causal decision theory thinks that the question of what to do turns on causal, rather than probabilistic, dependence, and and it is the subjunctive conditionals above, rather than their indicative counterparts, that track causal dependence.</span><br /><br /><span style="font-family: book antiqua, palatino;">The moral of our discussion is that the Control Hypothesis and causal decision theory have something important in common: they are both <em>causalist</em> accounts of their subject matters. Since indicative conditionals track probabilistic dependence rather than causal dependence, this means that when probabilistic dependence and causal dependence come apart, the Control Hypothesis and Causal Decision Theory will both count indicative conditionals relating actions to outcomes as irrelevant to their subject matters. </span><br /><br /></p>
</div>
</div>
<div class="vert vert-1" data-id="block-v1:MITx+24.118x+2T2020+type@video+block@bd87595ac71b406083765c4314a24393">
<div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-init="XBlockToXModuleShim" data-has-score="False" data-runtime-version="1" data-graded="False" data-usage-id="block-v1:MITx+24.118x+2T2020+type@video+block@bd87595ac71b406083765c4314a24393" data-runtime-class="LmsRuntime" data-block-type="video" data-request-token="8c3580a8035811efb61a02329aca76dd" data-course-id="course-v1:MITx+24.118x+2T2020">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Video"}
</script>
<h3 class="hd hd-2">Video Review: A connection with free will</h3>
<div
id="video_bd87595ac71b406083765c4314a24393"
class="video closed"
data-metadata='{"speed": null, "saveStateEnabled": false, "streams": "1.00:rrKFNRFp5C0", "savedVideoPosition": 0.0, "ytTestTimeout": 1500, "generalSpeed": 1.0, "poster": null, "publishCompletionUrl": "/courses/course-v1:MITx+24.118x+2T2020/xblock/block-v1:MITx+24.118x+2T2020+type@video+block@bd87595ac71b406083765c4314a24393/handler/publish_completion", "completionEnabled": false, "autoplay": false, "completionPercentage": 0.95, "captionDataDir": null, "duration": 0.0, "saveStateUrl": "/courses/course-v1:MITx+24.118x+2T2020/xblock/block-v1:MITx+24.118x+2T2020+type@video+block@bd87595ac71b406083765c4314a24393/handler/xmodule_handler/save_user_state", "ytApiUrl": "https://www.youtube.com/iframe_api", "start": 0.0, "transcriptLanguage": "en", "lmsRootURL": "https://openlearninglibrary.mit.edu", "prioritizeHls": false, "autoAdvance": false, "transcriptLanguages": {"en": "English"}, "autohideHtml5": false, "transcriptTranslationUrl": "/courses/course-v1:MITx+24.118x+2T2020/xblock/block-v1:MITx+24.118x+2T2020+type@video+block@bd87595ac71b406083765c4314a24393/handler/transcript/translation/__lang__", "transcriptAvailableTranslationsUrl": "/courses/course-v1:MITx+24.118x+2T2020/xblock/block-v1:MITx+24.118x+2T2020+type@video+block@bd87595ac71b406083765c4314a24393/handler/transcript/available_translations", "ytMetadataEndpoint": "", "recordedYoutubeIsAvailable": true, "sources": [], "showCaptions": "true", "end": 0.0}'
data-bumper-metadata='null'
data-autoadvance-enabled="False"
data-poster='null'
tabindex="-1"
>
<div class="focus_grabber first"></div>
<div class="tc-wrapper">
<div class="video-wrapper">
<span tabindex="0" class="spinner" aria-hidden="false" aria-label="Loading video player"></span>
<span tabindex="-1" class="btn-play fa fa-youtube-play fa-2x is-hidden" aria-hidden="true" aria-label="Play video"></span>
<div class="video-player-pre"></div>
<div class="video-player">
<div id="bd87595ac71b406083765c4314a24393"></div>
<h4 class="hd hd-4 video-error is-hidden">No playable video sources found.</h4>
<h4 class="hd hd-4 video-hls-error is-hidden">
Your browser does not support this video format. Try using a different browser.
</h4>
</div>
<div class="video-player-post"></div>
<div class="closed-captions"></div>
<div class="video-controls is-hidden">
<div>
<div class="vcr"><div class="vidtime">0:00 / 0:00</div></div>
<div class="secondary-controls"></div>
</div>
</div>
</div>
</div>
<div class="focus_grabber last"></div>
<h3 class="hd hd-4 downloads-heading sr" id="video-download-transcripts_bd87595ac71b406083765c4314a24393">Downloads and transcripts</h3>
<div class="wrapper-downloads" role="region" aria-labelledby="video-download-transcripts_bd87595ac71b406083765c4314a24393">
<div class="wrapper-download-transcripts">
<h4 class="hd hd-5">Transcripts</h4>
<ul class="list-download-transcripts">
<li class="transcript-option">
<a class="btn btn-link" href="/courses/course-v1:MITx+24.118x+2T2020/xblock/block-v1:MITx+24.118x+2T2020+type@video+block@bd87595ac71b406083765c4314a24393/handler/transcript/download" data-value="srt">Download SubRip (.srt) file</a>
</li>
<li class="transcript-option">
<a class="btn btn-link" href="/courses/course-v1:MITx+24.118x+2T2020/xblock/block-v1:MITx+24.118x+2T2020+type@video+block@bd87595ac71b406083765c4314a24393/handler/transcript/download" data-value="txt">Download Text (.txt) file</a>
</li>
</ul>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-init="VerticalStudentView" data-has-score="False" data-runtime-version="1" data-graded="False" data-usage-id="block-v1:MITx+24.118x+2T2020+type@vertical+block@a566b0e9ed6f4191b6e2dc0aead5c729" data-runtime-class="LmsRuntime" data-block-type="vertical" data-request-token="8c3580a8035811efb61a02329aca76dd" data-course-id="course-v1:MITx+24.118x+2T2020">
<h2 class="hd hd-2 unit-title">One more thing...</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+24.118x+2T2020+type@video+block@c3ab1019bc9645aab6239ed3683b5d9f">
<div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-init="XBlockToXModuleShim" data-has-score="False" data-runtime-version="1" data-graded="False" data-usage-id="block-v1:MITx+24.118x+2T2020+type@video+block@c3ab1019bc9645aab6239ed3683b5d9f" data-runtime-class="LmsRuntime" data-block-type="video" data-request-token="8c3580a8035811efb61a02329aca76dd" data-course-id="course-v1:MITx+24.118x+2T2020">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Video"}
</script>
<h3 class="hd hd-2">Video: A Newcomb Experiment</h3>
<div
id="video_c3ab1019bc9645aab6239ed3683b5d9f"
class="video closed"
data-metadata='{"speed": null, "saveStateEnabled": false, "streams": "1.00:mZjxLuhQ9y4", "savedVideoPosition": 0.0, "ytTestTimeout": 1500, "generalSpeed": 1.0, "poster": null, "publishCompletionUrl": "/courses/course-v1:MITx+24.118x+2T2020/xblock/block-v1:MITx+24.118x+2T2020+type@video+block@c3ab1019bc9645aab6239ed3683b5d9f/handler/publish_completion", "completionEnabled": false, "autoplay": false, "completionPercentage": 0.95, "captionDataDir": null, "duration": 0.0, "saveStateUrl": "/courses/course-v1:MITx+24.118x+2T2020/xblock/block-v1:MITx+24.118x+2T2020+type@video+block@c3ab1019bc9645aab6239ed3683b5d9f/handler/xmodule_handler/save_user_state", "ytApiUrl": "https://www.youtube.com/iframe_api", "start": 0.0, "transcriptLanguage": "en", "lmsRootURL": "https://openlearninglibrary.mit.edu", "prioritizeHls": false, "autoAdvance": false, "transcriptLanguages": {"en": "English"}, "autohideHtml5": false, "transcriptTranslationUrl": "/courses/course-v1:MITx+24.118x+2T2020/xblock/block-v1:MITx+24.118x+2T2020+type@video+block@c3ab1019bc9645aab6239ed3683b5d9f/handler/transcript/translation/__lang__", "transcriptAvailableTranslationsUrl": "/courses/course-v1:MITx+24.118x+2T2020/xblock/block-v1:MITx+24.118x+2T2020+type@video+block@c3ab1019bc9645aab6239ed3683b5d9f/handler/transcript/available_translations", "ytMetadataEndpoint": "", "recordedYoutubeIsAvailable": true, "sources": [], "showCaptions": "true", "end": 0.0}'
data-bumper-metadata='null'
data-autoadvance-enabled="False"
data-poster='null'
tabindex="-1"
>
<div class="focus_grabber first"></div>
<div class="tc-wrapper">
<div class="video-wrapper">
<span tabindex="0" class="spinner" aria-hidden="false" aria-label="Loading video player"></span>
<span tabindex="-1" class="btn-play fa fa-youtube-play fa-2x is-hidden" aria-hidden="true" aria-label="Play video"></span>
<div class="video-player-pre"></div>
<div class="video-player">
<div id="c3ab1019bc9645aab6239ed3683b5d9f"></div>
<h4 class="hd hd-4 video-error is-hidden">No playable video sources found.</h4>
<h4 class="hd hd-4 video-hls-error is-hidden">
Your browser does not support this video format. Try using a different browser.
</h4>
</div>
<div class="video-player-post"></div>
<div class="closed-captions"></div>
<div class="video-controls is-hidden">
<div>
<div class="vcr"><div class="vidtime">0:00 / 0:00</div></div>
<div class="secondary-controls"></div>
</div>
</div>
</div>
</div>
<div class="focus_grabber last"></div>
<h3 class="hd hd-4 downloads-heading sr" id="video-download-transcripts_c3ab1019bc9645aab6239ed3683b5d9f">Downloads and transcripts</h3>
<div class="wrapper-downloads" role="region" aria-labelledby="video-download-transcripts_c3ab1019bc9645aab6239ed3683b5d9f">
<div class="wrapper-download-transcripts">
<h4 class="hd hd-5">Transcripts</h4>
<ul class="list-download-transcripts">
<li class="transcript-option">
<a class="btn btn-link" href="/courses/course-v1:MITx+24.118x+2T2020/xblock/block-v1:MITx+24.118x+2T2020+type@video+block@c3ab1019bc9645aab6239ed3683b5d9f/handler/transcript/download" data-value="srt">Download SubRip (.srt) file</a>
</li>
<li class="transcript-option">
<a class="btn btn-link" href="/courses/course-v1:MITx+24.118x+2T2020/xblock/block-v1:MITx+24.118x+2T2020+type@video+block@c3ab1019bc9645aab6239ed3683b5d9f/handler/transcript/download" data-value="txt">Download Text (.txt) file</a>
</li>
</ul>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
© All Rights Reserved