# [EM] Range voting, zero-info strategy simulation

raphfrk at netscape.net raphfrk at netscape.net
Wed Nov 1 07:30:16 PST 2006

```> A. Sincere. This voter rates the candidates sincerely even if this means
> he doesn't use the top or bottom ratings.
> B. Maximized sincere. This is the same as A, except that the best and
> worst candidates are moved to the 10 and 0 positions, in order to
> maximize the weight between these two candidates.
> C. "Acceptables" strategy. The voter gives a 10 to every candidate worth
> 5 or more, and a 0 to the others. This can mean that the voter gives a
> 10 to every candidate, or a 0 to every candidate.
> D. Zero-info Approval strategy. The voter gives a 10 to every candidate
> at least as good as the average value of all candidates, and gives a
> 0 to the others.
>
> with S = 500000 (1000000 trials here)
> A: 0.000075
> B: 0.000088
> C: 0.000131
> D: 0.000174
>

I was thinking, has anyone looked at the effects of risk aversion on voter strategy?

In the above example, the voter might be faced with deciding which strategy to use:

A
75% of +1
25% of 0

Expected: 0.75

B
88% of +1
12% of 0

Expected: 0.88

C
31% of +2
69% of +1

Expected: 1.31

D
45% of -1
55% of +4

Expect: 1.75

A voter might be willing to use option C even though D gives a better expected value.

One way to include this is to try to maximise the expected value of the log of the outcome.

Assuming that the total utility of the person for each result is 5+(above utility), this works out as:

A
75% of +1 -> log(6)=0.78
25% of 0 -> log(5)=0.70

Expected: 0.76

B
88% of +1 -> log(6)=0.78
12% of 0 -> log(5)=0.7

Expected: 0.77

C
31% of +2 -> log(7)=0.84
69% of +1 -> log(6)=0.78

Expected: 0.80

D
45% of -1 -> log(4)=0.60
55% of +4 -> log(9)=0.95

Expect: 0.79

Option C wins despite option D having better expected value, due to risk aversion. The formula would mean that people would be more risk averse the larger a percentage of their wealth depends on the outcome of the election.

Also, the only reason that option D comes so close to winning is due to the fact that it has an expected utility that is nearly on third higher than option C.

The main point is that risk aversion could be the reason that in practice people drift away from perfectly strategic voting.

There are various functions that could be used to simulate risk aversion. Maximising the expected value of the log of the outcome is optimal for gambling. If the amount is small, it collapses to betting based on expected values. However, as a larger percentage of total wealth is at stake, it becomes risk averse.

The example given was:

Assuming that you start with \$1 and can place a bet on a fair coin. If you win, you get 1.05 times your stake (and your stake back). You get to repeat the gamble as often as you want, but can only use your initial stake and any money you win.

What is the optimal amount to bet in order to maximise the rate of income. Clearly, if you bet all your money you will with near certainty be bankrupt after say, 10 rounds.

Raphfrk
--------------------
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"what if anyone could modify the laws"

www.wikocracy.com

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