<HTML><BODY><font size="3">> A. Sincere. This voter rates the candidates sincerely even if this means<br>
> he doesn't use the top or bottom ratings.<br>
> B. Maximized sincere. This is the same as A, except that the best and<br>
> worst candidates are moved to the 10 and 0 positions, in order to<br>
> maximize the weight between these two candidates.<br>
> C. "<span class="correction" id="">Acceptables</span>" strategy. The voter gives a 10 to every candidate worth<br>
> 5 or more, and a 0 to the others. This can mean that the voter gives a<br>
> 10 to every candidate, or a 0 to every candidate.<br>
> D. Zero-info Approval strategy. The voter gives a 10 to every candidate<br>
> at least as good as the average value of all candidates, and gives a<br>
> 0 to the others.<br>
><br>
> with S = 500000 (1000000 trials here)<br>
> A: 0.000075<br>
> B: 0.000088<br>
> C: 0.000131<br>
> D: 0.000174<br>
> <br>
<br>
<br>
I was thinking, has anyone looked at the effects of risk aversion on voter strategy?<br>
<br>
In the above example, the voter might be faced with deciding which strategy to use:<br>
<br>
A<br>
75% of +1<br>
25% of 0<br>
<br>
Expected: 0.75<br>
<br>
B<br>
88% of +1<br>
12% of 0<br>
<br>
Expected: 0.88<br>
<br>
C<br>
31% of +2<br>
69% of +1<br>
<br>
Expected: 1.31<br>
<br>
D<br>
45% of -1<br>
55% of +4<br>
<br>
Expect: 1.75<br>
<br>
A voter might be willing to use option C even though D gives a better expected value.<br>
<br>
One way to include this is to try to <span class="correction" id="">maximise</span> the expected value of the log of the outcome.<br>
<br>
Assuming that the total utility of the person for each result is 5+(above utility), this works out as:<br>
<br>
A<br>
75% of +1 -> log(6)=0.78<br>
25% of 0 -> log(5)=0.70<br>
<br>
Expected: 0.76<br>
<br>
B<br>
88% of +1 -> log(6)=0.78<br>
12% of 0 -> log(5)=0.7<br>
<br>
Expected: 0.77<br>
<br>
C<br>
31% of +2 -> log(7)=0.84<br>
69% of +1 -> log(6)=0.78<br>
<br>
Expected: 0.80<br>
<br>
D<br>
45% of -1 -> log(4)=0.60<br>
55% of +4 -> log(9)=0.95<br>
<br>
Expect: 0.79<br>
<br>
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.<br>
<br>
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.<br>
<br>
The main point is that risk aversion could be the reason that in
practice people drift away from perfectly strategic voting.<br>
<br>
There are various functions that could be used to simulate risk aversion. <span class="correction" id="">Maximising</span>
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.<br>
<br>
The example given was:<br>
<br>
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.<br>
<br>
What is the optimal amount to bet in order to <span class="correction" id="">maximise</span> the rate of income. Clearly, if you bet all your money you will with near certainty be bankrupt after say, 10 rounds.<br>
<br>
<span class="correction" id="">Raphfrk</span><br>
--------------------<br>
Interesting site<br>
"what if anyone could modify the laws"<br>
<br>
<span class="correction" id="">www</span>.<span class="correction" id="">wikocracy</span>.<span class="correction" id="">com</span><br>
<br>
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