You are right that your process (each party knocks out 15/31) is in effect equivalent to Borda where majority votes first then minority responds, assuming that each group votes as a bloc. So why not just use Borda with all votes publicly revealed simultaneously? There's some ways to try to game the system if you think you can guess the other party's votes. But the majority has far more to lose than to gain by guessing wrong, so they'll probably just take a safe honest strategy; and then the minority can, if they wish, choose the majority-party winner by top-ranking them. In other words, you'd get good results by the majority voting honestly and the minority voting strategically on one candidate and honestly on all others.<div>
<br></div><div>What do you think?</div><div><br></div><div>Jameson<br><div><br><div class="gmail_quote">2012/11/19 Andy Jennings <span dir="ltr"><<a href="mailto:elections@jenningsstory.com" target="_blank">elections@jenningsstory.com</a>></span><br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">Jameson,<div><br></div><div>Your solution to the original problem (use an anonymous voting system) is not a bad one, but it is still interesting to consider the problem where the voting system is not anonymous and going against your caucus is indeed punishable behavior. Suppose the caucus loyalty is so strong that the entire majority party votes as a bloc. What voting systems will still elect some kind of compromise candidate?</div>
<div><br></div><div>With all of our top-tier methods (Range, Approval, MJ, Condorcet), there is a defined way for a majority bloc to vote that will ensure their outcome no matter how the minority votes. IRV too.</div><div>
<br></div><div>Interestingly enough, Borda Count can give us a compromise winner in this situation, if the majority votes first and the minority can see the totals and vote reactively. The majority can't put enough distance between their chosen winner and the other candidates to knock them all out of the running. In effect, they must leave N candidates within striking distance and then, if the minority unites, they can elect any one of those candidates. I haven't had the time to calculate N. It depends on the size of the majority and the minority as well as how many candidates there are. My thinking was that if that's how the game theory works out (majority nominates N candidates and the minority chooses between them) then why not just make that process explicit? Tell the majority to nominate N candidates and then let the minority choose between them. Then we can choose the number N directly, we're not limited to the one that falls out of the Borda construction.</div>
<div><br></div><div>This method can still choose the median leader without instituting anonymity or challenging caucus loyalty. I'm just not sure, yet, how it extends to more than two parties.</div><span class="HOEnZb"><font color="#888888"><div>
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~ Andy</div></font></span><div class="HOEnZb"><div class="h5">
<div class="gmail_extra"><br><br><div class="gmail_quote">On Mon, Nov 12, 2012 at 1:32 PM, Andy Jennings <span dir="ltr"><<a href="mailto:elections@jenningsstory.com" target="_blank">elections@jenningsstory.com</a>></span> wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">Good thoughts, Jameson.<div><br></div><div>I think you are right that if voting was anonymous and a good voting system were used, it would turn out pretty well. Also, it is necessary that *running* for leadership not be a punishable offense. The easiest way to fix this, I think, is to say that every legislator is in the running for leadership and you can't opt out. Would those two structural changes be enough, then?</div>
<div><br></div><div>More thinking about the original proposal:</div><div><br></div><div>What if both parties, in their caucus and using whatever voting system they wanted, nominated 16 legislators for leader. Then there will be at least one legislator approved by both parties. (If there is more than one, then hold approval voting runoffs in the whole legislature, or something.) This is pretty close to my earlier proposals, and I don't think the incentive to nominate turkeys would be all that great.<br>
<br>If there were three parties, you could have each party nominate 21 people so there is at least one legislator approved by all three parties. This is equivalent to allowing each party to eliminate 10 people. You do these eliminations sequentially, largest party to smallest party, or the reverse. Or you could let each party eliminate one at a time, in ten rounds, until there was only one left. But any of these options seems to give a big advantage for a party with just under a minority to split into two parties.<br>
</div><div><div><div class="gmail_extra"><br><br><div class="gmail_quote">On Mon, Nov 12, 2012 at 5:33 AM, Jameson Quinn <span dir="ltr"><<a href="mailto:jameson.quinn@gmail.com" target="_blank">jameson.quinn@gmail.com</a>></span> wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">Why not just use approval voting (or MJ) within the legislature? The problem with the "nominate 16 and we'll pick one" idea (and the like) is that it gives a strong incentive to nominate candidates that, for whatever reason, everyone knows are unsuitable.<div>
<br></div><div>To me, the basic way that the approval voting could go wrong is if voting outside your caucus were a punishable betrayal. So, I think you'd need to have a secret ballot. That's unfortunate for ordinary voters, who generally should have the right to know what their representatives are doing in their name. But other than that, I think that the incentives are pretty good, and it would settle on a capable near-median candidate.<br>
<div><br></div><div>Jameson<br><br><div class="gmail_quote">2012/11/11 Andy Jennings <span dir="ltr"><<a href="mailto:elections@jenningsstory.com" target="_blank">elections@jenningsstory.com</a>></span><br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
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<div>What would be the ideal way to choose leaders in a legislature?</div><div><br></div><div>In the Arizona house and senate, for example, once our legislators are elected, the majority party caucuses to choose the leadership. Assuming the Hotelling model, let's say they end up choosing the median legislator on their half of the political spectrum. It follows that the legislature will be led by someone from about the 25th percentile on the political spectrum. Then, if the other party gains control, the leadership will swing to the 75th percentile on the political spectrum. Wouldn't it be much better we could force the leadership to be near the median of elected legislators?</div>
<div><br></div><div>In the Arizona senate, for example, which has thirty members, the majority party may have as few as seventeen members and the caucus could be controlled by nine, or thirty percent of the senate. I'm not sure, but I have to imagine that this is common.</div>
<div><br></div><div>Here are some ways to force the leadership near the median (assume a legislative body of 31 members and just two parties, for now):</div><div><br></div><div>1. "The majority party shall nominate 16 senators for president and the minority party shall choose among them."</div>
<div><br></div><div>2. "The minority party shall nominate 16 senators for president and the majority party shall choose among them."</div><div><br></div><div>I think either of those would tend to choose a president near the median. Is one better than the other? Is it possible to extend to multiple parties? Without forcing them to form a majority coalition first?</div>
<div><br></div><div>Say there are three parties. Should each party, in turn, eliminate ten people? Does the largest party or the smallest go first?</div><div><br></div><div>Or should the first party eliminate 15 and then the other parties choose among the remaining 16 via approval voting or something?</div>
<div><br></div><div>Other ideas?</div><span><font color="#888888"><div><br></div><div>~ Andy</div>
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