I’ve been toying with the idea of creating something that uses Prospect Theory. Prospect Theory grew out of Utility Theory, which is described pretty succinctly in Thinking Fast and Slow. The creator of Utility Theory, Nicolas Bernoulli, was troubled by a scenario he imagined, called the St. Petersburg Paradox. Here’s a breakdown of the paradox, according to eConport.org (http://www.econport.org/econport/request?page=man_ru_basics2):

Suppose you were made an offer. A fair coin would be tossed continuously until it turned up tails. If the coin came up tails on the nth toss, you would receive $2n, i.e. if it came up tails on the 5th toss, you would receive $2^5 = $32. Of course, the first step is to calculate the expected value of the gamble: The probability of the coin turning up tails on the nth toss (which is, of course, equal to the probability of it turning up heads) equals 1/2n. So the expected value of the gamble would be: (1/2) * 2 + (1/4) * 4 + (1/8) * 8 + (1/16) * 16 + ….. = 1 + 1 + 1 + 1 + …… and on till infinity.

Bernoulli attempted to solve to try and find the amount that would make this gamble “worth it.” Basically, what was a rational (in a mathematical sense only) amount of money to pay to flip a coin before it pays off? Here’s the formula Bernoulli came up with:

u(w) = k log(w) + constant


eConport.org points out that w = amount of money, and k = a parameter. U = the utility of the money, “or the subjective, internal value they attach to an additional unit of money is determined by how much money they already have – the value a homeless person would attach to a hundred-dollar bill is far more than Bill Gates would.” It also points out that Bernoulli used a logarithmic function because the utility should decrease as the actual value increases (i.e., if you are rich, larger amounts of money mean less to you).

There’s a chart showing the expected payout of each coin toss based on a k value of 1 and a constant of 0, but I don’t think I can upload it until my WordPress site is up. Just know that apparently the amount you should pay to play the Bernoulli paradox with those values is $4, which seems pretty good.

Here’s when Prospect Theory comes in: most people would not play this coin flip game. Never mind that flipping this coin over and over would be tedious (but again, rationally: worth it). People don’t think like this. More often than not, people don’t consider what they have to gain when making a risky choice; they are considering what they have to lose. And their considerable losses are based on how they’re doing right now. This can apply to wealth, or mood, or anything that’s considered a “value” when trying to calculate happiness. Here’s how Economist Thayer Watkins (http://www.sjsu.edu/faculty/watkins/prospect.htm) describes the Prospect Theory established by Daniel Kahneman and Amos Tversky:

Subjects, when offered a choice formulated in one way, might display risk-aversion but when offered essentially the same choice formulated in a different way might display risk-seeking behavior. For example, as Kahneman says, people may drive across town to save $5 on a $15 calculator but not drive across town to save $5 on a $125 coat. This probably seems like common sense to most people–you are saving more of the $15 than you are of the $125 coat.

But think about it. In both scenarios, you are saving $5. That amount of money shouldn’t be compared to the price of the item in question — it should be compared to the amount of money you stand to save, since that’s your hard-earned money you’re spending. Watkins goes on:

One very important result of Kahneman and Tversky’s work is demonstrating that people’s attitudes toward risks concerning gains may be quite different from their attitudes toward risks concerning losses. For example, when given a choice between getting $1000 with certainty or having a 50% chance of getting $2500 they may well choose the certain $1000 in preference to the uncertain chance of getting $2500 even though the mathematical expectation of the uncertain option is $1250.


This is a perfectly reasonable attitude that is described as risk-aversion. But Kahneman and Tversky found that the same people, when confronted with a certain loss of $1000 versus a 50% chance of no loss or a $2500 loss do often choose the risky alternative. This is called risk-seeking behavior. This is not necessarily irrational but it is important for analysts to recognize the asymmetry of human choices.

So, when considering what they have to gain, people tend to be conservative. They tend to be risk-averse. But when considering what they might lose, people are risk-prone. They want to do everything they can to protect themselves from loss, including taking risks they wouldn’t have taken when they only had the option to gain something. As Watkins says, this isn’t necessarily irrational. There’s no use trying to put a judgement on our decision-making process as a species–we probably evolved to think this way for a perfectly good reason. But it is a super interesting thing to consider in the context of designing digital user interfaces, since those are basically tiny digital places where dozens of micro-decisions (sometimes very risky ones!) play out.

The most interesting part of Prospect Theory, in my opinion, is the consideration of “Reference Points”. This is how Daniel Kahneman describes reference points in his and Tversky’s 1979 paper on Prospect Theory:

The evidence discussed in the previous section shows that people normally perceive outcomes as gains and losses, rather than as final states of wealth or welfare. Gains and losses, of course, are defined relative to some neutral reference point.


The reference point usually corresponds to the current asset position, in which case gains and losses coincide with the actual amounts that are received or paid. However, the location of the reference point, and the consequent coding of outcomes as gains or losses, can be affected by the formulation of the offered prospects, and by the expectations of the decision maker.

Basically, not only do people think of risks in terms of utility, like Bernoulli proposed, they think of it in terms of a specific reference point (their starting wealth, their starting mood, their starting number of friends), not the outcome. Studies based on prospect theory show that we are much more likely to take risks when we are trying to avoid a loss, as not losing something (as it is perceived to us, based on our reference point) is way more attractive to us that gaining something (as it is perceived to us, based on our reference point).

So, anyways. What does this have to do with my thesis? I would like to try and break Prospect Theory. I want to create digital interfaces that are attractive in the way places that spin risk often are. I want to try and make people feel like they should be risk-averse when facing a potential loss, and risk-prone when facing a potential gain, but in a digital environment. I think this is what casinos do. By appearing attractive (bright! shiny! bustling!) enough, I’m hoping that I can combat people’s regular reactions to risk taking. So, if I have a plain-as-can-be interface, where a user knows they have a certain sum of money, and the interface presents an option to gamble that, according to Prospect Theory, should make them make a risk-averse decision, would they be affected at all if the interface wasn’t as plain? Maybe they won’t choose differently, but would they hesitate? Would they take more time to consider the risk? What if the interface presents certain colors? Certain pictures? Certain sounds? There’s an extremely, extremely simplified visual example in this folder.

I understand that changing the visual and sonic presentation of a digital interface probably won’t have any effect on how people take risks. But I want to know if I can get some understanding of how our senses of sight and hearing may help guide us in digital environments where we’re taking risks.

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