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added hw1 and updated reading
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‎index.html

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@@ -145,7 +145,7 @@ <h2 id="schedule">Schedule</h2>
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<td>
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Decision-making and Probability
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<ul>
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<li>Reading: <a href="homeworks/review-prerequisite.html">Probability</a></li>
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<li>Reading: <a href="https://docs.google.com/document/d/1GiQUL71Iv2iGEe5hRy5yxTNQijA-fpWV9qcJucbwPVc/edit?usp=sharing" target="_blank">Decision-theory and Probability</a></li>
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<!-- <li><a href="https://docs.google.com/a/uw.edu/presentation/d/1iMX_Q-yQooYkkLZMiOn80h-8tO82TI1Z0f-VdK1DWDo/edit?usp=sharing">Welcome</a> (10 min)</li> <!-- I'm experienced -->
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<!-- <li>Review this syllabus (20 min)</li> -->
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<!-- <li>Activity (40 min): <a href="activities/situating-software-organizations.html">Situating software organizations</a></li> -->
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<p>Each day in class we'll practice some skill. You'll get <a href="#grading">0.5 points</a> if you engage in and complete the activity. How to get credit for the activity will depend on the activity; sometimes being present will be enough, sometimes being to class on time will be enough, and sometimes you'll have to turn something in.</p>
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<h2 id="reading">Reading</h2>
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<p>To access the readings, you will do the following:</p>
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<ol>
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<li>Click on the reading (a link to a Google doc) on the <a href="#schedule">course schedule</a></li>
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<li>Copy the google doc to your personal INFO 370 folder (which we shared with you at the beginning of the course). <a href="https://support.google.com/docs/answer/49114" target="_blank">Instructions on making a copy of a file in Google Drive.</a></li>
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<li>Read through the google doc/reading. Highlight and <a href="https://support.google.com/docs/answer/65129" target="_blank">comment</a> any parts which are confusing.</li>
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<li>Complete the questions marked "TODO".</li>
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</ol>
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<p>
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You should complete your readings and reflection survey<i>before</i> at the beginning of each lecture (twice a week).
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You should complete your readings and reflection <i>before</i> at the beginning of each lecture (twice a week).
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Each time, you'll come prepared to discuss the assigned reading.
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</p>
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<li>We discuss the correct answers as a class.</li>
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</ul>
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<p>Your answer is correct, you'll receive <a href="#grading">1 point</a>. We will give partial credit for partially correct answers, at our discretion.</p>
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<p>
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You will receive <a href="#grading">0.5 points</a> for completing the reading and reflection before class (on the Google Doc).
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You will receive up to another 0.5 points for getting the in-class reading quiz correct.
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We will give partial credit for partially correct answers on the reading quiz, at our discretion.
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In total, you can receive up to 1 point per reading.
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</p>
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<h2 id="homework">Individual Homework</h2>
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‎readings/decision-making-and-probability.html

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@@ -33,7 +33,7 @@ <h2>Decision are Choices, Outcomes, and Values of Outcomes</h2>
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Making decisions is about choosing the options that leads to the outcome with the highest total value.
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In business scenarios one might predict a dollar amount for the value for each possible outcome.
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In a personal or other scenario one might imagine how much something is worth in dollars and use that as a value (or otherwise use numbers to express how much one wants an outcome);
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note that this is potentially error-prone / inappropriate, but let’s (potentially dangerously) assume someone takes the time to carefully consider how much that outcome is worth to them and gives it a dollar amount.
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note that this is potentially error-prone / inappropriate, but let's (potentially dangerously) assume someone takes the time to carefully consider how much that outcome is worth to them and gives it a dollar amount.
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</p>
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<h3>When each choice has a certain outcome</h3>
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For example, on my way to class I walk by someone selling chocolate. I might consider this decision quickly as:
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</p>
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<table class="table table-striped text-left">
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<tr>Table 1: Value given choice</tr>
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<tr>
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<td><b>Choice</b></td>
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<td><b>Outcome</b></td>
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<td><b>Value</b></td>
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</tr>
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<tr>
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<td>Buy chocolate</td>
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<td>I eat chocolate</td>
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<td>"+$10" in happiness</td>
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</tr>
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<tr>
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<td>Do not buy chocolate</td>
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<td>I do not eat chocolate</td>
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<td>$0</td>
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</tr>
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</table>
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<p>
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With this way of describing the choice, choosing to buy chocolate will lead to a higher-value outcome - a benefit "equivalent" to $10 from eating chocolate. Why $10? Well I just really like chocolate and I think I will be about as happy as if I had found $10 on the ground. Thus, choosing buy chocolate would optimize my potential value from the decision (gain $10 in value vs. gain $0).
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</p>
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<h3>When each choice also has a cost</h3>
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<p>
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As I go to buy the chocolate, I realize the chocolate costs money - $5. I reconsider my values for each outcome, subtracting the costs of making that choice.
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</p>
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<table class="table table-striped text-left">
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<tr>Table 2: Value given choice and costs</tr>
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<tr>
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<td><b>Choice</b></td>
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<td><b>Outcome</b></td>
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<td><b>Value</b></td>
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</tr>
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<tr>
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<td>Buy chocolate</td>
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<td>I eat chocolate</td>
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<td>+$10 (in happiness) - $5 (cost) = +$5 net benefit</td>
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</tr>
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<tr>
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<td>Do not buy chocolate</td>
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<td>I do not eat chocolate</td>
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<td>$0</td>
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</tr>
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</table>
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<p>
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Buy chocolate still has the highest valued outcome at $5, so I reach for my wallet. However, I suddenly realize I'm not so sure there's only one possible outcome from that choice.
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When there are many possible outcomes that are unknown / uncertain
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Really, most decisions in life do not have a guaranteed outcome. Each choice can have multiple possible outcomes. In our example we'll add another possible outcome.
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Looking over the person selling chocolate, I realize I don't know them, I haven't seen them before, and they are wearing a strange costume. I add a new outcome (I leave the value entry blank if that outcome cannot happen for that choice).
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</p>
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<table class="table table-striped text-left">
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<tr>Table 3: Value given choices with uncertain outcomes</tr>
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<tr>
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<td></td>
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<td colspan="3" class="text-center">Outcomes</td>
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</tr>
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<tr>
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<td></td>
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<td><b>Eat nothing</b></td>
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<td><b>Eat chocolate</b></td>
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<td><b>Eat poisoned chocolate, go to hospital</b></td>
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</tr>
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<tr>
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<td>Choice: Buy chocolate</td>
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<td>n/a</td>
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<td>+$10 (happiness) - $5 (cost) = $5 (net benefit)</td>
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<td>-$1000 (hospital) - $5 (chocolate) = -$1005 (net benefit)</td>
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</tr>
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<tr>
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<td>Choice: Do not buy chocolate</td>
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<td>$0</td>
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<td>n/a</td>
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<td>n/a</td>
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</tr>
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</table>
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<p>
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Now that there are multiple outcomes, there are different rules I might use to decide. Here are two fairly extreme rules:
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</p>
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Decision Rules:
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<ul>
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<li><b>Minimize the worst possible outcome</b>: Take the worst outcome for each choice, then choose the choice with the best (of the worst) outcomes.</li>
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<li><b>Maximize the best possible outcome</b>: Take the best outcome for each choice, then choose the choice with the best (of the best) outcomes.</li>
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</ul>
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<p>
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For minimize the worst possible outcome, I'd choose to not buy chocolate.
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To maximize the best possible outcome, I'd choose to buy the chocolate.
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</p>
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<h3>When you're biased and inadvertently change your analysis to get the choice you want</h3>
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<p>
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Now, the thought occurs to me, that maybe I'll eat half of the chocolate, meet someone that looks hungry on the way,
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share my chocolate, start up a wonderful conversation, one thing leads to another, and - fast forward 10 years into the future
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- we're a happy couple and life is awesome. I add a new outcome to my decision table.
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</p>
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<table class="table table-striped text-left">
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<tr>Table 4: Value given choices with uncertain outcomes</tr>
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<tr>
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<td></td>
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<td colspan="4" class="text-center">Outcomes</td>
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</tr>
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<tr>
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<td></td>
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<td><b>Eat nothing</b></td>
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<td><b>Eat chocolate</b></td>
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<td><b>Eat poisoned chocolate, go to hospital</b></td>
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<td><b>Share chocolate with my future partner</b></td>
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</tr>
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<tr>
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<td>Choice: Buy chocolate</td>
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<td>n/a</td>
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<td>+$10 (happiness) - $5 (chocolate) = $5 (net benefit)</td>
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<td>-$1000 (hospital) - $5 (chocolate) = -$1005 (net benefit)</td>
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<td>$10,000,000 (happiness) - $5 (cost) = $9,999,995 (net benefit)</td>
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</tr>
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<tr>
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<td>Choice: Do not buy chocolate</td>
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<td>$0</td>
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<td>n/a</td>
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<td>n/a</td>
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<td>n/a</td>
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</tr>
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</table>
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<p>
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Now, the two decision rules from before seems really unsatisfactory.
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If I try to, I can probably think about extreme outcomes (bad or good) for any choice I make,
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which can heavily influence the choice I "should" make based on those rules.
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</p>
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<h2>Expressing belief with probability</h2>
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<p>
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Play this game to get a feel for subjectively expressing belief as a probability distribution
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<a href="http://cassandraxia.com/projs/advbiases/" target="_blank">Adventures in Cognitive Biases</a>
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</p>
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<h2>Decision theory</h2>
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<p>
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Decision theory combines the choices-outcomes-values model of a decision along with a probability distribution of the outcomes for each choice.
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Practitioners of orthodox (prevalent / accepted) decision theory recommend one choose the choice that has the highest "expected" value, adjusted for the probability of that outcome. For example, for the decision below with the following probabilities:
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</p>
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<table class="table table-striped text-left">
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<tr>Table 5: Probability table for chocolate outcomes</tr>
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<tr>
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<td><b>Choice</b></td>
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<td><b>Outcome</b></td>
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<td><b>Probability</b></td>
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</tr>
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<tr>
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<td>Buy chocolate</td>
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<td>Eat chocolate</td>
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<td>0.99</td>
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</tr>
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<tr>
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<td>Buy chocolate</td>
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<td>Eat poisoned chocolate</td>
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<td>0.009999</td>
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</tr>
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<tr>
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<td>Buy chocolate</td>
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<td>Share chocolate with future partner</td>
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<td>0.000001</td>
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</tr>
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<td>Buy chocolate</td>
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</tr>
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</table>
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<p>
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We can make our decision by first calculating our expected outcome, the product of the value of each outcome with the likelihood of it occuring.
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<math>1+1</math>
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</p>
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<p>
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Decision analysis without probability can change based on unlikely or extreme outcomes.
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In general, it can be hard to define all the possible outcomes; decision analysis tends to just focus on some set of outcomes.
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Some people in the decision analysis community try to come up with ways to deal with possible outcomes, this but limiting outcomes is a fundamental limitation of the method.
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In the end, it's hard to tell if you have included all the possible choices and possible outcomes that matter in an analysis.
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</p>
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<h2>Further Reading</h2>
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<p>
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<i>Dutch book</i> arguments: If you don't use fair rules, someone can trick you into buying bets that you can't ever profit from.
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</p>
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<p id="cherubini">Cherubini, M., Venolia, G., DeLine, R., & Ko, A. J. (2007, April). <a href="https://doi.org/10.1145/1240624.1240714">Let's go to the whiteboard: how and why software developers use drawings</a>. In Proceedings of the SIGCHI conference on Human factors in computing systems (pp. 557-566).</p>
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‎style.css

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table.text-left td {
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}
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table td.text-center{
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text-align: center;
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