Suneet Singal on expected value without fake precision

Suneet Singal's page on expected value explains a piece of arithmetic and then refuses to dress it up as science. It belongs with the decisions essays beside the podcast The Opportunity Notebook with Suneet Singal. Expected value is a weighted average of outcomes, where each weight is a probability. The Stanford Encyclopedia of Philosophy states the idea as a normative account of choice under uncertainty: a way to rank acts when you do not know which result will arrive. This entry copies that structure with a labeled hypothetical. Every probability and every score in the example is invented for the lesson. None of them is a research finding, a market forecast, or advice from Suneet Singal, whose published professional background is in real estate and corporate finance. The arithmetic is useful when the inputs are honest and the units are named. It becomes theater when someone adds decimals the evidence cannot support.

A weighted average, not a prophecy

Expected value is arithmetic for a choice whose result you do not yet know. You list the outcomes you are treating as the possibilities. You give each outcome a value in a unit you can explain. You give each outcome a probability, a weight between zero and one. You multiply each value by its probability, and you add the products. The sum is the expected value of that option. The Stanford Encyclopedia of Philosophy, in its entry on expected utility, describes the same structure as a normative theory: a theory about how to rank acts when you are unsure, whose slogan is to choose the act with the highest expected utility. Utility, in that theory, is a numerical measure of how much an outcome is preferred. This page will often say score instead of utility, because a homemade score is not a scientific utility. It is a local stand-in so the multiplication is visible.

The phrase expected does not mean predicted. An expected value of 5 does not mean the result will be 5. If the outcomes are 10 and 0, each with probability one half, the expected value is 5, and 5 itself may be an outcome that cannot happen. The 5 is a summary of the gamble, useful for comparing this gamble with another. It is not the fortune teller's answer. Kahneman's Nobel work, and the later Harvard Business Review article with Lovallo and Sibony, is full of warnings about how people handle uncertainty. One warning this page adds, in ordinary language, is that a summary feels like a fact. It is only as good as the list, the scores, and the probabilities you put in.

Suneet Singal is not the source of the formula, and this page does not attach it to any deal in his real estate or corporate finance background. The podcast The Opportunity Notebook with Suneet Singal is the neighboring public work. The formula is a public piece of decision theory. Use it when you have a real partition of outcomes and weights you are willing to defend. Refuse it when you want a number to end an argument that is actually about values.

The arithmetic in a labeled hypothetical

This is a labeled hypothetical. Every figure in it was invented for the lesson. It is not a weather study, not a survey, and not a recommendation. A neighborhood club is deciding whether to set up an outdoor reading on Saturday. For the exercise, they consider two outcomes of setting up, and they pretend these two exhaust the possibilities. Dry afternoon: they score the day at 8, because the reading happens and the setup felt worth it. Rainout: they score the day at -3, because they hauled chairs for nothing and the indoor plan was disrupted. They judge, for the exercise only, that the dry outcome has probability 3/4 and the rainout has probability 1/4. Those two weights add to 1, which is what you want when the outcomes are meant to cover the whole chance.

The expected value of setting up, inside the exercise, is (3/4) times 8, plus (1/4) times -3. Three quarters of 8 is 6. One quarter of -3 is -0.75. The sum is 5.25. The alternative, in the same exercise, is not setting up and doing the indoor sorting they already planned, which they score at 0. Inside the fiction, 5.25 is higher than 0, so the arithmetic ranks setting up above sorting, if and only if the club really accepts the scores and the weights. Say that sentence in full. The number 5.25 does not outrank anybody by itself. It restates the inputs. Change the rainout score to -30, because the chairs belong to a neighbor who will be angry, and the sum becomes (3/4) times 8 plus (1/4) times -30, which is 6 minus 7.5, or -1.5. Now the arithmetic ranks sorting higher. The lesson is the sensitivity, not the 5.25.

Write the unit next to the score. In this story the unit is the club's own points, not dollars, not lives, and not utility measured in a laboratory. If you cannot say what a point means, do not add points. A later section shows a second comparison with the same discipline. None of these calculations is a finding about outdoor events. If you run a real reading, make your own list, your own scores, and your own weights, and label them as judgments.

The inputs are judgments

Probabilities in this kind of personal or organizational choice are usually judgments, not frequencies you counted. A frequency, when you have one, is a gift: out of the last twenty similar Saturdays, how many rained in a way that would have wrecked the reading? If you have that count, you have a base rate, and the base-rate page is the place to think about whether those twenty Saturdays are the right class. If you do not have the count, your 3/4 is a judgment. Judgments can be sincere and still be wrong. The arithmetic does not correct them. It preserves them and gives them a polished surface. Kahneman, Lovallo, and Sibony ask where the numbers came from, because anchored and optimistic numbers slide into recommendations. Ask that question of every weight before you multiply.

Scores are judgments too. An 8 means someone preferred the dry reading to the rainout by that margin on a scale they chose. Another member may score the dry reading at 2 because they dislike crowds. Expected value will then rank the options differently, and the math will not referee the disagreement. The disagreement is about values. Put it in words. Averaging people's scores can be a clerical step, and it can also hide a real split about the point of the club. Do not average away a conflict you have not named. The page on whose definition of success you are using is the right room for that conflict. Expected value starts after the unit of success is shared.

There is a further judgment in the list of outcomes. Two outcomes are a model. The real Saturday might be dry and poorly attended, or rainy and strangely wonderful. If an outcome you left off would change the ranking, the model is too small. Add it, or admit that you are calculating a simplified world. The encyclopedia entry is clear that the theory ranks acts given the outcomes, probabilities, and utilities you have specified. It does not go out and check that you specified the right world. That check is your responsibility, and it happens in sentences, before the multiplication.

Fake precision

Fake precision is what you get when rough inputs produce a result that looks measured. The weights 3/4 and 1/4 are already coarse. Reporting the result as 5.2500 pretends the inputs had a precision they did not have. Even 5.25 is more costume than the inputs deserve if the 8 and the -3 were picked in a minute. A honest report sounds like this: using scores of about 8 and about -3, and a judgment that a dry afternoon is roughly three times as likely as a rainout, setup ranks above the indoor plan. If we score the rainout as a serious harm, the ranking flips. The ranking is the product. The decimals are optional, and often dishonest.

Intervals beat point illusions. If the club thinks the dry probability is somewhere between 1/2 and 4/5, compute both ends with the same scores. At 1/2, expected value is (1/2) times 8 plus (1/2) times -3, which is 4 minus 1.5, or 2.5. At 4/5, it is 6.4 plus -0.6, or 5.8. Both ends, in this invented sheet, still beat 0. That is a more useful sentence than a single 5.25: inside this range of weights, the ranking is stable. If one end had fallen below 0, the honest sentence would be that the ranking depends on a probability we do not know tightly. Uncertainty about the ranking is a result. Do not bury it under one displayed number.

Money does not cure the problem. Replacing points with dollars lets people import a unit they recognize, and it tempts them to invent dollar values for things that are not prices. The anger of a neighbor is not a market quote. If you put it in dollars, label the translation as a judgment. A labeled judgment of we would pay up to $40 to avoid that mess is different from a fake invoice. This page will not supply a translation table, because any table of that kind would be invented research. Keep the unit local, or use money only where money is actually what you will gain or lose.

What the number does not decide

Expected value ranks options inside a model. It does not decide whether the model counted everything that matters. A higher expected value can sit on top of a one-way door, a cruel residue, or a success definition the group never adopted. The number is an input to the decision sentence, not a replacement for it. A club can look at 5.25, still judge that the neighbor's chairs make the door too heavy, and stay inside. That is not a failure to understand the arithmetic. It is a refusal to let one model consume the other questions on these pages: reversibility, the next ring of effects, the premortem, the checklist.

The theory also does not say that a good expected value guarantees a good Saturday. You may set up, get the rainout, and score -3. The decision can still have been the better gamble given what you knew. Reread the page on definitions of success if that sentence feels like an excuse. It is a distinction, not an excuse. Grade the decision against the information and the alternatives you had. Grade the outcome against what happened. Then ask whether the scores or the weights should change before the next Saturday. Updating is allowed. Pretending you knew the rain in advance is not.

If two options are close, say they are close. A 5.25 against a 5.1 is not a revelation if both numbers came from minute-long judgments. Call it a tie and decide with the other considerations: which option is easier to undo, who bears the residue, which one the group can explain in a sentence. Close expected values are a reason to stop calculating, not a reason to add another decimal. Hammond, Keeney, and Raiffa, in their article on even swaps, offer a different way to compare alternatives across several objectives without forcing everything into one fragile number. You do not have to use their full method to accept the warning. One number is a compression. Compressions throw information away. Know what you threw away.

A second labeled comparison

This is still the same labeled hypothetical, with a third option added so the comparison is richer. The club can also run a short indoor reading that needs no chairs from the neighbor. They score it at 4 if attendance is decent and at 1 if almost nobody comes. For the exercise only, they put probability 1/2 on each of those two indoor outcomes. The expected value of the indoor reading is (1/2) times 4 plus (1/2) times 1, which is 2 plus 0.5, or 2.5. Compare the three invented summaries. Outdoor setup: 5.25, and it flips to -1.5 if the rainout is scored at -30. Indoor reading: 2.5, and it does not depend on the weather. Sorting: 0. If the club believes the mild rainout score, outdoor ranks first. If the club believes the severe rainout score, indoor ranks first. Sorting ranks last in both of these particular sheets, which is not a general truth about sorting. It is a feature of the scores they wrote.

Lay the sheet out in words before anyone types it into a spreadsheet. Spreadsheets hide the judgments in cells and display the sum in a larger font. The larger font is how fake precision wins. A sheet that fits on the decision memo, with the probabilities labeled as judgments and the scores labeled as the club's points, is the right size. If a member wants to change a weight, change it in the meeting and recompute in front of everyone. The arithmetic is simple enough to do on paper. If it has become too complex to recompute while people watch, the model has more moving parts than the decision can support.

The second comparison also shows why a single option's expected value is incomplete. 5.25 means nothing until you see 2.5 and 0 beside it. Expected value is for ranking acts, as the encyclopedia says. An act alone does not have a practical meaning. Rank at least the live alternatives, including the alternative of leaving the afternoon as it already was. Leaving things alone often has no advocate, and a spreadsheet will omit it unless someone types it in. Give it a row.

When to refuse the calculation

Refuse the calculation when you have no outcomes you can name, when you are using it to drown a disagreement about purpose, or when the probabilities are being invented to reach a result someone already wants. A confirmatory expected value is easy to build. Choose scores until the favorite wins, then display the sum. The checklist question from Kahneman, Lovallo, and Sibony, about where the numbers came from, is the right interruption. If the answer is we adjusted them until the outdoor plan won, throw the sheet out. If the answer is these are our judgments, and here is the range that would flip the ranking, keep the sheet.

Refuse extra precision in public. Say roughly, say the ranking flips if the bad case is scored as a serious harm, say the weights are judgments. Do not say the model gives 5.25 and therefore the science supports us. There is no science in the hypothetical, and there is no science in your local sheet unless you brought real counts and said so. Base rates, when you have them, can inform the weights. They do not appear by wishing. If you do not have them, the weight stays a judgment and should look like one.

Then decide with the rest of the record. The expected-value line on the memo is one line. The decision sentence, the definition of success, the door, the opportunity cost, and the next ring are other lines. A club that can say, in one breath, that outdoor ranks higher only under the mild score, that the chairs make a heavier door, and that they will therefore run the indoor reading this week, has used the arithmetic properly. They let it rank a model. They did not let it pretend to be the world. That restraint is the whole meaning of expected value without fake precision.

What this entry does not claim

Suneet Singal’s published professional background is in real estate and corporate finance. Company filings linked from this site record a chief executive officer departure from FC Global Realty Incorporated effective 2 January 2018 and an acting chief executive officer appointment at First Capital Investment Corporation effective 12 September 2017. The Suneet Singal Scholarship, Grant and Giving websites describe him as the founder of those programs. This entry explains a general subject. It is not a private track record, a current job title, an investment result, or a quote.

Weights that come from how often a kind of result happens belong on base rates. The thing you give up to chase a higher score is opportunity cost. A single Saturday judged alone is narrow framing.