Lottery – our cunning little ‘Swiss army knife’?

Randomness – using a lottery – can be a crafty little tool in many ways other than selecting Citizens Juries. How it works depends on human psychology. We know what selection by lottery is meant to do – keep Human Judgement out of it! Or to put it more formally: it is either its ‘sanitizing’ effect (Peter Stone) or the arrationality effect (Olly Dowlen).

But human psychology comes into it as well. Which is more valuable – a gift of 1 Euro or a lottery ticket with a 1 in a 1,000,000 chance of  500,000 Euro?

Easy, say you hyper-rational kleroterians! Take the money.

Not so! The General Public are quite happy to buy tickets every week for such a lottery with an expected loss of 50% of your stake. There’s something about lottery prizes that makes them more valuable than the expected  prize – and can also make a small loss more painful than a large gain. The statistician Jimmy Savage discovered these ‘irrational’ traits of the human mind when developing Decision Theory.

Administrators have made use of this property of the lottery to design more efficient methods to nudge (very fashionable idea at the moment!), lure or dupe people into particular forms of behaviour:

–In China “Sales Tax Lotteries” increased sales taxes collected by 17%. Every purchase has a simple “Lotto Serial Number” on the digital receipt. The ability to print that serial number requires registration and remitting sales tax. A percentage of the sales taxes collected would be used to pay randomly selected sales tax receipts.

–In the Netherlands it’s not just places for medical school that use a lottery! To cut down on absenteeism, a large Dutch manufacturer set up a lottery: “If you took no days off for the last 3 months, you go into a lottery. There are 7 prizes of 75 Euro each.” The lottery turned out to be highly beneficial to the firm. It would have cost far more in individual pay-outs to achieve the reduction in absenteeism, compared to the cost of the lottery.

I can even remember a UK pub chain which invited you to ‘check your receipt’ to see if there was a star printed on the back. If so you won a free drink! Cunningly this was a crafty way to control the bar-tenders and make sure that every sale went through the till. (Needless to say my receipt didn’t win).

Marketeers use this ploy as well – complete this questionnaire, and you might win a Ferrari!

What’s going on here? It’s good old human ‘irrationality’ which values the chance of a big prize more highly than its expected value. There’s something, too, which makes a lottery prize less degrading compared to a straight cash payment.

It’s as well to remember its counterpart – loss-aversion. The result  of losing a big prize – like a place at Medical School – may be a  cause of great psychological pain — ‘Regret’ was Savage’s word for it.

So let’s not forget: don’t just be rational — it’s the effect on the human psyche of Our Cunning Little Tool of randomness that really counts!

7 Responses

  1. > We know what selection by lottery is meant to do – keep Human Judgement out of it! Or to put it more formally: it is either its ‘sanitizing’ effect (Peter Stone) or the arrationality effect (Olly Dowlen).

    To me the role of the lottery in the context of sortition is not to keep judgement out, it is to make the selected subset representative of the population – to harness the law of large numbers.


  2. Exactly — this is the opposite of arationality, it’s a highly rational process, seeing as it’s based on a predictable statistical relationship between the sample and the target population. If a random sample in the high hundreds wasn’t roughly 50%/50% male/female then there would be something wrong with the sampling procedure. In his book, Peter claims that representation is a subset of arationality, but this is clearly not true. However Conall’s interest here is with psychological irrationality, rather than statistics. So it would seem that the swiss army knife is both arational, rational and irrational at the same time.


  3. That’s the thing about ‘tools’ (or mechanisms) like the lottery. They can be used in many ways, and for different reasons. Other tools too, might have the same effect. But one thing is certain — the outcome of a fair lottery cannot be controlled by human agency.


  4. >the outcome of a fair lottery cannot be controlled by human agency.

    Not so if you posit a notion of aggregate (group) agency. A conservative (or “liberal”) predisposition in the country will “fix” the lottery so that it will be biased towards those that share this predisposition. This is anything but random, as it short-circuits the Dowlen “blind break” principle. But that’s why Yoram and myself are attracted to the rational predictability of the lottery to accurately mirror the underlying characteristics of the population that it is seeking to represent. If the nation is prejudiced in favour of (say) gay marriage then an allotted assembly seeking to determine public policy on this matter will be predisposed to legislate in its favour — the only proviso being that the assembly will be obliged to think about it first (and hear opposing views) before coming to its decision. But the decision won’t be a random one, it will be heavily weighted by the pre-lottery disposition of the target population. If this were not true, and the lottery just returned a random verdict (bypassing “human agency”) then we might as well legislate randomly by examining the entrails of a chicken, tea-leaves in a cup, or consulting the Delphic oracle.


  5. Keith, forgive me, but I have no idea what you are talking about. Your claim that…

    “Not so if you posit a notion of aggregate (group) agency. A conservative (or ‘liberal’) predisposition in the country will ‘fix’ the lottery so that it will be biased towards those that share this predisposition. This is anything but random, as it short-circuits the Dowlen ‘blind break’ principle.”

    …you are at best playing fast and loose with my argument–at best. What you say does not in any way challenge the caim that lotteries cannot be controlled by human agency. The area in which agency is excluded is in the selection of the random sample. It is obviously NOT excluded at the level of the agents selected. The idea–which I would have thought obvious–was that you want the random sample to use reasons, but you don’t want reasons used to select those in the sample. If 60% of the population support some idea, then 60% of the sample will as well (provided the sample is large enough). But that 60% can only figure into the behavior of the sample, not the selection of the sample itself. That’s the level, obviously, at which human agency is kept out. To claim that this fact proves that the lottery is “fixed” makes no sense at all.

    Now, it’s a separate argument whether descriptive representation–
    which I obviously acknowledge is ensured via random selection–can be accounted for by a theory which focuses upon the exclusion of reasons from the selection process. I think it can, you disagree, fine. (It’s always nice to see you and Yoram agree on something!) But I cannot see anything close to a basis for denying that lotteries are uncontrollable by human agency, and that is part of their appeal. What am I missing here?


  6. Peter

    The lottery is fixed in the sense that, at the aggregate level, it’s possible to predict with a very high level of certainty that a sizeable sample will contain approx. 50% females — this is determined by the lottery process and it is a quality that short-circuits the “blind break”. It’s hard to understand what could be more rational than this — please explain to us how it’s possible to subsume this within your overall (arational) “lottery principle”.

    Whether or not something is rational or arational depends on the level of analysis. Sortition may be arational at the level of which individuals are chosen, but at the aggregate level it is 100% rational, hence my adoption of terms like collective agency. There are any number of examples from nature of behaviours that appear random at the individual level, but if you zoom out to the collectivity (swarm, anthill, hive etc) you can see that each individual is part of a larger pattern. Exactly the same thing is true in a lottery — the selection of one individual female is entirely random, but if the lottery is big enough then the law of large numbers dictates that 50% of the sample will be female. Thus the process is arational at the individual level but rational at the aggregate level.


  7. Putting it slightly differently, it’s perfectly possible for a lottery to select, say, one female and 999 males from a balanced population of 100 million or so. However this is extremely unlikely because the results are fixed by the invisible hand of the Law of Large Numbers (LLN). LLN is a uber-rational goddess with a passionate interest in equal rights and this is the reason why she is so vital to all of us with an interest in the lot as a way of implementing democratic equality for those who FAIL to draw the golden ticket. It’s not just that we all have an equal chance of winning and losing (social justice), it’s that those of us who lose will still be represented by our invisible proxies (democracy), and the number of proxies will correspond exactly to our numerical strength in the larger population. Not for LLN the arbitrary whims of Zeus and the other members of the old pantheon (and the uber-rational divine being LLN doesn’t even require sacrificial propitiation).

    Those of us who are interested in the lot as a democratic tool (C&P, Yoram, myself and a few others) wouldn’t mind if the worshippers of the Lottery Principle were to acknowledge the existence of other deities. But they are, on the whole, intolerant monotheists. Olly Dowlen does consider sortition as a tool for democratic representation but dismisses it as a “weak” use of the lot (huh?), whereas Peter Stone doesn’t consider it at all (the word “representation” not appearing in the index of his book). When pushed on the topic Peter argues that our god (LLN) is a minor underling of the one true god — the sacred principle of the Arational Being. We, of course, acknowledge arationality, but our main concern is that the RATIO of salient features within the microcosm should be the same as in the whole population and only deviate from this principle when Rational Ignorance starts to show his evil presence. Of course the atheists and humanists within our community (it’s a broad church) don’t like to talk of divine beings (or Platonic principles) like LLN and prefer to think of her as some form of collective HUMAN agency.* But, whatever your metaphysical preferences, the important thing is that LLN fixes the results of the lottery by traversing the Blind Break — were it not so sortition would be of no interest at all from a democratic point of view.

    * The dispute between Platonists (like Roger Penrose) and constructivists in mathematical theory is of relevance here.


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