I don't think I've expressed my "pivotal voter" argument very well. Warren's response clearly points to some holes in what I've <i>said</i>, but I think my underlying argument is still firm.<div><br>
</div><div>So before responding point-by-point, let me try again to say what I'm trying to get at.</div><div><br></div><div>Assume a chicken scenario: a plurality-winner condorcet-loser "opposition" X, and two near-clones Y and Z, of whom Z is the Condorcet winner. Typically, Z will also be the winner under honest score or honest medians.</div>
<div><br></div><div>In a median system with sufficient resolution, Y voters know that, if all other votes are held constant, any vote they might consider for Z falls into one of six classes:</div><div>-group γ: Y is winning anyway, so there is no need to consider strategy.</div>
<div>-group 0: Bottom rank. This risks electing X if the Z voters are similarly uncooperative.</div><div>-group 1: Below the medians of both Y and Z, but above bottom rank. Strategy could not help elect Y. The only effect it could have would be to encourage voters in future elections to be more strategic. That would be more likely to favor X, and almost as likely to favor Z, as it would be to favor Y; so on the whole, strategy is NOT in the Y voters interests in either short or long term.</div>
<div>-group 2: Below the median of Z but above that of Y. In this case, strategy would not help directly, but it could be seen as opening up "strategic room" for the voter(s) in group 3 to swing the election. Still, the same considerations as group 2 apply, and so strategy is not favored on the whole.</div>
<div>-group 3, "pivotal": At Z's median. In the limit of infinite precision votes, this will only be true for one voter. For this voter, *if* group 2 is empty due to strategy, then strategizing will be strategically favored until they reach the second-bottom rating, or below Y's median, whichever is higher. If group 2 is not empty, though, strategy will not be favored, except perhapes expressively; dropping their vote to the next lowest Z rating will shrink Z's margin of victory.</div>
<div>-group 4: Above Z's median: Such a voter could in theory gain a strategic advantage by leapfrogging below the median vote. However, the fact that they are considering a vote above the median means that, compared to group 3, their strategic advantage is less and the strategic risk of going to bottom-rating is greater. </div>
<div><br></div><div>In my initial post in this thread, I perhaps did not emphasize clearly enough that voters will NOT know which class their honest vote would fall into. But they do know that logically it must fall into one of the above classes. The voters who have the most intrinsic motivation to use strategy will be very same ones who will also know that they are most likely to fall into groups γ, 1, and 2 — which happen to be the ones which gain no advantage whatsoever from strategy. The voters with the least motivation to be strategic will know that they most likely fall into group 3, for whom subcritical strategy (dropping to second-to-bottom rating) is unlikely to work (unless group 2 has all chosen strategy) and extreme strategy (dropping to bottom-rating) is most dangerous (with the lowest benefits and the highest risks). And in general, all voters will know that they are very unlikely to happen to be the one pivotal voter in group 3.</div>
<div><br></div><div>Now, clearly a given Y voter will not necessarily know which of those classes their honest Z vote would fall into. But the strategic situation is significantly different from Score (and approval) in two key aspects:</div>
<div><br></div><div>-difference 1: Those with the most to gain and the least to lose from strategy (groups 1 and 2) are the least likely to have it have any effect. Therefore, it is significantly more plausible that these voters will vote honestly; and in that case, such honesty will almost certainly cascade to the less-strategically-motivated voters in groups 3 and 4.</div>
<div>Another way of putting this same advantage is: while in Score, if the honest margins are slim, the most-strategically-motivated voters can cause a pathological win by X, in median systems, it takes participation from some of the less-strategically-motivated.</div>
<div>-difference 2: There is a "subcritical" strategy option which, as long as it is used by a minority of voters, is just as powerful as extreme strategy; but which, in all cases, is safe against a pathological result. </div>
<div><br></div><div>Note that difference 1 is likely to keep more voters honest, and that reinforces the likelihood that difference 2 will apply: a majority of voters will be honest, and so subcritical strategy will be just as effective and far safer.</div>
<div><br></div><div>Note also that subcritical strategy is less likely to spur a vicious cycle of spiteful retaliation. Many experiments show that humans have a far greater tendency for such spiteful retaliation than pure short-term rationality would dictate; various models explain this in terms of evolutionarily-favored meta-rationality. But I expect that subcritical strategy will be seen more as "minimal cooperation" than as backstabbing, and so will prompt less retaliation.</div>
<div><br></div><div>Is any of this getting clearer?</div><div><br></div><div>So, to respond to Warren specifically:</div><div><br></div><div><br></div><div><div class="gmail_quote">2013/6/2 Warren D. Smith (CRV cofounder, <a href="http://RangeVoting.org">http://RangeVoting.org</a>) <span dir="ltr"><<a href="mailto:warren.wds@gmail.com" target="_blank">warren.wds@gmail.com</a>></span><br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">Seems to me, much (all?) strategic voting is done by people who are not thinking "I will perform this <div>strategy and the other voters will do nothing" but more like "a zillion voters like me will perform strategy along with me plus there will be many other counter-strategizing voters."</div>
</blockquote><div><br></div><div>For voters who expect to be in groups 1 or 2, that doesn't change the situation. I agree that such thinking would apply to groups 3 and 4; but I think at least part of group 4 would not have enough in common with group 3 to sympathize with them.</div>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div><br></div><div>In such a situation, notions of the the (one) "pivotal voter" become pretty irrelevant.</div>
<div><br></div><div>Also, in the event there is (with a median-based rating method) "1-sided strategy" then what happens is, the first strategizer moves the median, then the subsequent voters move it more, etc. As a result of that synergy</div>
<div>the 456552th strategizer is motivated to exaggerate in his vote even though, say, if he had</div><div>been the only one, then there would have been zero such motivation.</div></blockquote><div><br></div><div>But the first strategizer is in group 1, and doesn't move the median. It's not until you run through all of groups 1 and 2 that this feedback begins. That builds a firewall against strategic feedback.</div>
<div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div><br></div><div><div class="im"><blockquote class="gmail_quote" style="margin:0;margin-left:0.8ex;border-left:1px #ccc solid;padding-left:1ex">
<div>>What does that mean for the strategic dynamics of the chicken dilemma? It means that, in a very real >sense, those two pivotal voters are the only ones under "strategic pressure".</div></blockquote>
<div>
<br></div></div><div>--so, that quote strikes me as absurdly far away from and irrelevant to the real world.</div></div></blockquote><div><br></div><div>Fair enough; that was poorly expressed.</div><div><br></div><div>Jameson </div>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div><span class="HOEnZb"><font color="#888888"><div><br></div><blockquote class="gmail_quote" style="margin:0;margin-left:0.8ex;border-left:1px #ccc solid;padding-left:1ex">
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