I'd be interested in running an behavioral-economics-type experiment on voting behavior. I imagine a game matrix of 9 voters and 3 candidates, with each candidate having a known payout for each player. For each condition, we'd have a separate group of experimental subjects. We'd run two non-binding "pre-election polls" and one "election", and then pay real money for the payout. I could put up the money, create the experimental protocol, and program a web app to run the elections, but I'd like help actually getting diverse sets of subjects. I imagine three payoff matrices (positive, zero, and negative sum; see below) and up to six voting systems (approval, range, MJ, SODA, condorcet for negative sum, and IRV for positive sum), for a total of 11 conditions. The payoff matrices would be as follows:<div>
<div><font class="Apple-style-span" face="'courier new', monospace"><span class="Apple-tab-span" style="white-space: pre; "> </span><span class="Apple-tab-span" style="white-space: pre; "> </span>Group<span class="Apple-tab-span" style="white-space:pre"> </span>Size<span class="Apple-tab-span" style="white-space:pre"> </span>Candidate<span class="Apple-tab-span" style="white-space:pre"> </span></font></div>
<div><font class="Apple-style-span" face="'courier new', monospace">Scenario 1 (zero-sum)<span class="Apple-tab-span" style="white-space:pre"> </span>A<span class="Apple-tab-span" style="white-space:pre"> </span>B<span class="Apple-tab-span" style="white-space:pre"> </span>C</font></div>
<div><font class="Apple-style-span" face="'courier new', monospace"><span class="Apple-tab-span" style="white-space: pre; "> </span><span class="Apple-tab-span" style="white-space: pre; "> </span>a<span class="Apple-tab-span" style="white-space:pre"> </span></font><span class="Apple-style-span" style="font-family: 'courier new', monospace; ">4<span class="Apple-tab-span" style="white-space:pre"> </span>4<span class="Apple-tab-span" style="white-space:pre"> </span>1<span class="Apple-tab-span" style="white-space:pre"> </span>0</span></div>
<div><font class="Apple-style-span" face="'courier new', monospace"><span class="Apple-tab-span" style="white-space: pre; "> </span><span class="Apple-tab-span" style="white-space: pre; "> </span>b<span class="Apple-tab-span" style="white-space:pre"> </span>2<span class="Apple-tab-span" style="white-space:pre"> </span>0<span class="Apple-tab-span" style="white-space:pre"> </span>3<span class="Apple-tab-span" style="white-space:pre"> </span>2</font></div>
<div><font class="Apple-style-span" face="'courier new', monospace"><span class="Apple-tab-span" style="white-space: pre; "> </span><span class="Apple-tab-span" style="white-space: pre; "> </span>c<span class="Apple-tab-span" style="white-space:pre"> </span>3<span class="Apple-tab-span" style="white-space:pre"> </span>0<span class="Apple-tab-span" style="white-space:pre"> </span>2<span class="Apple-tab-span" style="white-space:pre"> </span>4</font></div>
<div><font class="Apple-style-span" face="'courier new', monospace"><span class="Apple-tab-span" style="white-space: pre; "> </span><span class="Apple-tab-span" style="white-space:pre"> </span>Total payout<span class="Apple-tab-span" style="white-space:pre"> </span>16<span class="Apple-tab-span" style="white-space:pre"> </span>16<span class="Apple-tab-span" style="white-space:pre"> </span>16</font></div>
<div><font class="Apple-style-span" face="'courier new', monospace"><br></font></div><div><font class="Apple-style-span" face="'courier new', monospace">Scenario 2 (positive-sum CW)<span class="Apple-tab-span" style="white-space:pre"> </span>A<span class="Apple-tab-span" style="white-space:pre"> </span>B<span class="Apple-tab-span" style="white-space:pre"> </span>C</font></div>
<div><font class="Apple-style-span" face="'courier new', monospace"><span class="Apple-tab-span" style="white-space: pre; "> </span><span class="Apple-tab-span" style="white-space: pre; "> </span>a<span class="Apple-tab-span" style="white-space:pre"> </span>4<span class="Apple-tab-span" style="white-space:pre"> </span>3<span class="Apple-tab-span" style="white-space:pre"> </span>1<span class="Apple-tab-span" style="white-space:pre"> </span>0</font></div>
<div><font class="Apple-style-span" face="'courier new', monospace"><span class="Apple-tab-span" style="white-space: pre; "> </span><span class="Apple-tab-span" style="white-space: pre; "> </span>b<span class="Apple-tab-span" style="white-space:pre"> </span>2<span class="Apple-tab-span" style="white-space:pre"> </span>0<span class="Apple-tab-span" style="white-space:pre"> </span>3<span class="Apple-tab-span" style="white-space:pre"> </span>1.5</font></div>
<div><font class="Apple-style-span" face="'courier new', monospace"><span class="Apple-tab-span" style="white-space: pre; "> </span><span class="Apple-tab-span" style="white-space: pre; "> </span>c<span class="Apple-tab-span" style="white-space:pre"> </span>3<span class="Apple-tab-span" style="white-space:pre"> </span>0<span class="Apple-tab-span" style="white-space:pre"> </span>2<span class="Apple-tab-span" style="white-space:pre"> </span>3</font></div>
<div><font class="Apple-style-span" face="'courier new', monospace"><span class="Apple-tab-span" style="white-space: pre; "> </span><span class="Apple-tab-span" style="white-space:pre"> </span>Total payout<span class="Apple-tab-span" style="white-space:pre"> </span>12<span class="Apple-tab-span" style="white-space:pre"> </span>16<span class="Apple-tab-span" style="white-space:pre"> </span>12</font></div>
<div><font class="Apple-style-span" face="'courier new', monospace"><br></font></div><div><font class="Apple-style-span" face="'courier new', monospace">Scenario 3 (negative-sum CW)<span class="Apple-tab-span" style="white-space:pre"> </span>A<span class="Apple-tab-span" style="white-space:pre"> </span>B<span class="Apple-tab-span" style="white-space:pre"> </span>C</font></div>
<div><font class="Apple-style-span" face="'courier new', monospace"><span class="Apple-tab-span" style="white-space: pre; "> </span><span class="Apple-tab-span" style="white-space: pre; "> </span>a<span class="Apple-tab-span" style="white-space:pre"> </span>4<span class="Apple-tab-span" style="white-space:pre"> </span>4<span class="Apple-tab-span" style="white-space:pre"> </span>0.5<span class="Apple-tab-span" style="white-space:pre"> </span>0</font></div>
<div><font class="Apple-style-span" face="'courier new', monospace"><span class="Apple-tab-span" style="white-space: pre; "> </span><span class="Apple-tab-span" style="white-space: pre; "> </span>b<span class="Apple-tab-span" style="white-space:pre"> </span>2<span class="Apple-tab-span" style="white-space:pre"> </span>0<span class="Apple-tab-span" style="white-space:pre"> </span>3<span class="Apple-tab-span" style="white-space:pre"> </span>2</font></div>
<div><font class="Apple-style-span" face="'courier new', monospace"><span class="Apple-tab-span" style="white-space: pre; "> </span><span class="Apple-tab-span" style="white-space: pre; "> </span>c<span class="Apple-tab-span" style="white-space:pre"> </span>3<span class="Apple-tab-span" style="white-space:pre"> </span>0<span class="Apple-tab-span" style="white-space:pre"> </span>1<span class="Apple-tab-span" style="white-space:pre"> </span>4</font></div>
<div><font class="Apple-style-span" face="'courier new', monospace"><span class="Apple-tab-span" style="white-space: pre; "> </span><span class="Apple-tab-span" style="white-space:pre"> </span>Total payout<span class="Apple-tab-span" style="white-space:pre"> </span>16<span class="Apple-tab-span" style="white-space:pre"> </span>11<span class="Apple-tab-span" style="white-space:pre"> </span>16</font></div>
</div><div><font class="Apple-style-span" face="'courier new', monospace"><br></font></div><div><font class="Apple-style-span" face="arial, helvetica, sans-serif"><br class="Apple-interchange-newline">These scenarios present both a chicken dilemma between candidates B and C, and a contrast between a strong (for positive sum) or weak (for negative sum) Condorcet winner (candidate B). </font></div>
<div><font class="Apple-style-span" face="arial, helvetica, sans-serif"><br></font></div><div><font class="Apple-style-span" face="arial, helvetica, sans-serif">To save money and subjects, the four voters of voter group A could be represented by 2 actual experimental subjects with double-weighted votes. Thus, the total subjects necessary for a full set of 14 experimental conditions would be 98. Ideally, we'd run at least one scenario for each of the voting methods twice; thus we could also use up to 140 subjects. For 98 subjects, the total payout would be at most 234 monetary units, but probably under 200. Here in Guatemala, for a 30-minute experiment like this, those monetary units could probably be 1-2 quetzales ($0.13-$0.26); in the US, they would have to be $1-2, for a total payout cost of up to $400. Again, I'd put up that money.</font></div>
<div><font class="Apple-style-span" face="arial, helvetica, sans-serif"><br></font></div><div><font class="Apple-style-span" face="arial, helvetica, sans-serif">If you're interested, we'd have to talk about creative ways to get subjects and space. The best would be if there were someone here who is an undergraduate (at an undergrad-focused college) or a graduate student (at a university), who could get access to a pool of psych-101 student guinea pigs. Obviously, even then, getting a hundred subjects is not just a matter of asking for them; but with some coordination, I think we could manage it.</font></div>
<div><font class="Apple-style-span" face="arial, helvetica, sans-serif"><br></font></div><div><font class="Apple-style-span" face="arial, helvetica, sans-serif">Once the experiment was done, we could write it into a paper, including also mathematical discussion and proofs, simulations, and historical analysis; and I'm confident that we could get published. Yes, the statistics would be weak, perhaps too weak to really discern behavioral differences between Approval, Range, and MJ even if such differences exist; but I'm sure that no matter what happens, the results would advance our knowledge. I don't care whether I am counted as the primary author on that paper.</font></div>
<div><font class="Apple-style-span" face="arial, helvetica, sans-serif"><br></font></div><div><font class="Apple-style-span" face="arial, helvetica, sans-serif">Jameson</font></div><div><font class="Apple-style-span" face="arial, helvetica, sans-serif"><br>
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