Post No.: 0610

Furrywisepuppy says:

‘Cumulative prospect theory’ (and its predecessor ‘prospect theory’) modifies classical economic utility theory to take into account real human decision-making behaviours – particularly by accounting for reference points from which gains/losses are compared against. In cumulative prospect theory, decision weights for gains/losses aren’t assumed to be equal i.e. losses generally loom larger than gains (loss aversion).

Psychophysics is the field of psychology that studies subjective sensations in relation to stimulus intensities (e.g. the frequency of a tone and its subjective pitch, or an amount of money and its value). And for many dimensions of sensation and perception, ‘Weber’s Law’ states that the just-noticeable difference between two stimuli is roughly proportional to the magnitude of the stimuli (e.g. if you can sense a change of weight of 1kg on a 10kg bag of kibble, then you should be able to sense a change of weight of 2kg on a 20kg bag of kibble. That’s a mountain of kibble!)

Meanwhile, for many other dimensions, the function is roughly logarithmic according to ‘Fechner’s Law’ (e.g. if raising the number of LEDs from 1 to 4 increases subjective brightness by 1 unit, then raising the number of LEDs from 4 to 16 will increase subjective brightness by another 1 unit. That’s log base 4 in this case, which is what I’d be unloading in the garden if I ate that much kibble – woof!)

‘Stevens’s power law’ and a power law relationship is said to supersede the above law. This doesn’t matter too much here because the primary point is that we tend to care more about percentage changes rather than absolute changes. So a 20% increase in income will evoke a fairly similar response for both poor and rich people, whilst a £200 increase will evoke a greater response for the poor than the rich. The higher one’s initial wealth, the lower the psychological response to a change of given absolute wealth – which suggests that utility is a logarithmic function of wealth, rather than a weighted average of all the possible outcomes or the expected value.

A doubling of GDP should yield about the same increment of average life satisfaction in poor and rich countries alike. (Other factors might mean this is oversimplistic in reality though.) The same psychological distance separates £100,000 from £1M, and £10M from £100M i.e. there’s a diminishing marginal value or diminishing utility or sensitivity of wealth. This means that acquiring more money will increase happiness but with rapidly diminishing returns. Plus if one factors in the opportunity costs then those many extra hours and additional stresses at work for that little bit more won’t be worth, say, neglecting your family or health for.

So with a more holistic broad frame view – at a certain point, that little bit of increase in happiness from wanting a lot more money will be counterbalanced or possibly outweighed by a decrease in happiness for having to likely give up or neglect other parts of one’s life and the likely added stress of this on one’s health. Happiness therefore tends to effectively plateau beyond a certain income level.

In the reverse way when examining the costs of losses (as opposed to the benefits of gains), a poorer person will be more affected by a £10,000 loss than a richer person – hence why it’s poorer people who tend to need to buy insurance, and it’s richer people who sell it. Transferring risk is what insurance is all about, and poorer people will accept paying a premium (i.e. higher than the expected value) to transfer this risk onto richer people, and richer people will of course happily exploit this fact! (Realise also that buying insurance, when reframed, is essentially the same as placing a bet that something bad will happen i.e. you’ll have lost money if you don’t make a claim that’s worth more than the premium paid plus interest.)

…But the above picture of prospect theory is incomplete – we cannot just factor where people are but where they came from. A person who gained £80,000 from a starting point of £20,000 will feel a lot happier than a person who lost £80,000 from a starting point of £180,000, even though they both now have £100,000 each. In fact, even if the first person gained only £40,000 to now have £60,000, he/she’ll likely feel happier than the second person).

Therefore we think in terms of relative gains and losses, rather than merely absolute states. Utility, happiness or subjective sensation is determined by recent changes relative to one’s previous state – or a reference point. This includes what’s considered ‘hot’, ‘sweet’, ‘loud’ or even ‘blue in colour’, etc..

So the utility of a gamble depends not only on the weighted average of all the potential outcomes but also on one’s current position. Accordingly, the worst option rationally might still be attractive for a person who has a terrible starting point – this is why poor people will more likely stick with a low but sure gain on a game show rather than gamble for more, even when the expected value of the gamble is larger (e.g. a £3,000 sure gain will make a huge difference to their life already, perhaps to pay off some debts, even though they could take a 50:50 gamble on winning £10,000 or £0 (expected value of £5,000) instead).

Likewise, regarding losses – this is why already-rich people can take overly reckless gambles because they know that they can afford to lose big. Wealthy people won’t feel as much emotional response to losing/gaining a few thousand pounds.

If any gambles are worth only pennies or involve only tiny changes in utility then we will more likely deviate from the rational choice. Our attitude to risk won’t differ if our reference point is different by only minor amounts, but it’ll differ if it’s different by a lot.

Poor people therefore tend to be more risk-averse (e.g. taking the out-of-court settlement), whilst rich people tend to be more risk-seeking (e.g. taking it to court). This reference point bias affects how people sell stocks based on how much they initially bought them for, rather than based on the absolute gain/loss of a stock – the price they bought them for will be their reference point. Utility as a function of relative gains/losses is also a reason why bonuses escalate – as people become richer, they need bigger bonuses in order to feel the same utility from a bonus.

However, the psychological utility of gaining an amount is often different to the psychological disutility of losing the same amount. When all options are good, most people will be risk-averse and take the sure thing (e.g. when getting a guaranteed £900, or alternatively gambling on a 90% chance of getting £1,000 and a 10% chance of getting £0 – most people will take the first option). When both a gain and a loss are possible, most people tend towards risk-aversion or loss aversion too (e.g. when there’s a 50% chance of getting or losing £900 – most people won’t take this gamble). But when all options are bad, most people will be risk-seeking and take the gamble (e.g. when losing a guaranteed £900, or alternatively gambling on a 90% chance of losing £1,000 and a 10% chance of losing £0 – most people will take the second option. Because of diminishing sensitivity, the pain of a guaranteed loss of £900 is more than 90% of the pain of losing £1,000. One might need, perhaps, a 95% chance of losing £1,000 before the pain feels equal).

Both gains and losses exhibit diminishing sensitivity. So turning on a weak light in a dark room has a large effect, whilst turning on the exact same light in a bright room might be undetectable. Likewise, the subjective difference between £90 and £100 is much smaller than between £10 and £20 – hence people can inconsistently spend a lot of time and effort trying to save a few pounds off a cheap item yet be relatively blasé about shopping around to save many tens of pounds off their TV packages.

The reason why we like the idea of gaining £10 and dislike the idea of losing £10 isn’t because these amounts change our lives per se – we simply like winning and dislike losing, and most of us dislike losing more than we like winning due to loss aversion.

The probability itself (e.g. 98% versus 100%, or 2% versus 0%) also contributes to a predilection towards being more risk-averse due to the ‘certainty effect’ (where we prefer certainty over having the slightest doubt, hence why we might pay over the odds to get something 100% guaranteed), or more risk-seeking due to the ‘possibility effect’ (where we prefer having a remote rather than 0% chance, hence why we might play the lottery).

It’s therefore vital overall to not neglect reference points, like how much one already has. Super-rich people (even those who came from working-class backgrounds) can easily become out of touch with the rest of the population because they start to think that, say, £250,000 for doing a few speeches isn’t much after considering buying a piece of art worth £10M i.e. their reference points change. Shifting reference points happens to everyone though (e.g. portion sizes have crept up over the decades that one will likely think a regular portion size 30 years ago looks stingy nowadays). Unless one constantly recalibrates one’s reference points (e.g. by hanging around people who are on the breadline) then one’s reference points will drift. Unfortunately, most rich people only really hang around and compare with other rich people and thus easily become out of touch. But your life satisfaction partly depends on who or what you compare to (e.g. the millions of starving across the world or the handful of multi-billionaires in their mansions).

The decision whether to take a gamble or not is an act of ‘system two’ but the critical inputs for prospect theory are emotional responses generated by ‘system one’. The usual reference point is the status quo – one’s current state or a neutral point (adaptation level) – but it can also be the outcome that one expects or perhaps feels entitled to (e.g. the raise that one’s colleagues received or that’s been informally promised). Outcomes that are better than this reference point are considered gains, and vice-versa.

Both prospect theory and utility theory can fail though if the assumption of the reference point has a value of zero. Often it will be placed relative to one’s expectations or goal. So if you have a 85% chance of winning £1M and a 15% chance of winning £0 – although you came into this gamble with nothing to start with – to end up with nothing won’t feel like a non-event but will feel like a loss because of the high probability of winning and the huge value if you had won. Thus the value of a ‘zero’ outcome can change if it’s highly unlikely and/or when the alternative is highly valuable – disappointment, regret and the anticipation of these are real.

Even though a higher-ranked player may be slightly ahead in points in a game, they might feel unhappy because their reference point, their expectation, is to be much further ahead, hence they might regard that slight point advantage as more like a loss. When it comes to regret, the experience of an outcome depends on the options you could’ve took but didn’t, hence we don’t merely assess available options separately and independently and then pick the option with the highest value. If you’re presented a choice to either take a gamble with a 85% chance of winning £1M and a 15% chance of winning £0, or to take a sure £250,000 – the anticipated pain of losing the gamble is compounded by the regret of being greedy and missing out on the still decent alternative option… unless you’re filthy rich, out of touch and £250,000 means little to you that is(!)

Woof!

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