Statistics calling for inequity?

Jerome C. points us to this ad by the French car-marker Renault:

 For those who don't speak French (including me), this is a marketing campaign in which they will refund 1 out of every 300 car purchases, picked at random.

Jerome says:

How would it sound if a major car brand offered you a $50 rebate on a $15,000 car? ridiculous, and possibly insulting. Instead, car maker renault proposes to refund one car purchase out of 300. The ad campaign suggests that such an outcome is likely, compared to all the losing bets we are implicitly making every day. They are banking on the fact that this proposal is perceived as being more advantageous than typical discounts, although the expected value of the gambit is probably higher.

This lottery is no different from any lotteries out there. For positive outcomes, we tend to over-estimate the chance of success, something I discussed in Chapter 5. In any lottery, the average outcome (adjusted for probability of winning) is a useful number to summarize the universe of potential outcomes and to make a decision to play or not, but no player will win the "average" win; you either win the prize or you get nothing. Why would anyone play a lottery with negative expected return? There are lots of possible answers to this question. The one I like is: those who play like to think if someone has to win the lottery, then it would be me. (If you are the winner, the decision to play has been wise, in hindsight.)

In the case of Renault's campaign, Jerome considers the choice between a $50 rebate for everyone or a lottery offering a 1/300 chance to win a free car. One is a fair, equal distribution of spoils; the other, a winner-takes-all scheme.

Assume the expected values are the same. For Renault, the cash outlay would also be the same, assuming no difference in claim probability. But many customers probably prefer the lottery, the same people who buy lottery tickets every day. Jerome guesses, and I agree, that the latter would be more popular among customers, and thus have a higher marketing impact.

Comments

[HarlanH]

Interesting. I think it would work on me, if I were in the market for a Renault! The reason why is that I don't really care about $50 one way or the other. That rebate makes no difference to my standard of living at all, it's just rounding error in the 5-10 years I'll own the car. But 11,000 Euro is a lot of money, and winning would noticeably improve my quality of life!

This is an argument why, if you have to buy lottery tickets, you should buy the ones where the jackpot is millions, not just a few dollars or even a few hundred dollars. The expected return of buying a weekly lottery ticket is -$52/year, but that's also the most you can lose, while the best-case upside is unlikely, but quite large! Winning would seriously change your life!

(And if you're responsible with your money, it might even change it for the better!)

[gary]

If @HarlanH's intuition is correct - this appears to invert typical assumptions about risk-aversion that we get from finance: Given the same expected return, a rational person would prefer the one with less variance in outcomes. The issues of diversification (rational side) and scale (behavioral side) seem to play roles here.

[Kaiser]

Gary: I think the assumption in finance you're talking about is risk aversion. But then, I remember that one of the key insights from my investments class was that traders want volatility to make money, which has always led me to believe that the market is inherently unstable because the players profit from volatility.

[Danil]

See also: _Veeck as in Wreck_, _The Hustlers Handbook_.

Why give one ice cream sandwich to each fan, when you can give 5000 ice cream sandwiches to one fan, and give everybody else something they'll talk about for years....

[gary]

You can make money on volatility if you have an information advantage, diversification, or a long time horizon. You can seek risk if you believe you're able to bias results in your favor (e.g., stock quants, card counters). Or if you have a diversified portfolio so individual losses balance out, you can charge for taking on that risk from people who aren't able to do this (option selling, insurance). Or if you have a long time horizon, you can wait out volatility or even trade programmatically on dips (beware, you can get killed by black swans on both of the latter).

None of these apply to these lottery cases, but people are willing to take on that risk.

I believe pretty strongly in the behavioral component here - people don't accurately assess odds, people don't see the costs of entry (in this case, the $50 forgone rebate if it were given to every buyer), etc. That's why Renault goes the free car vs. trivial rebate route.

I just wonder if there's a theoretical explanation somewhere beyond/between "people are just stupid" and "people are purely rational" that explains where & how people will willingly absorb risk in the absence of any diversification, time horizon or informational advantages, and when they'll refuse.

We know from the behavioral studies that people will take $10 today vs. $11 tomorrow, but will take $11 in a month & a day over $10 in a month. So there's a threshold of time where people turn off their rational calculation of time value of money. What's the threshold for risk assessment?