Let me demonstrate this with an example. A much more reasonable & un-contrived example than the ones in the anti-Condorcet paper:
Voters' sincere preferences:
40%: Dole, Clinton, Nader 25%: Clinton 35%: Nader, Clinton, Dole
[The Clinton voters have no 2nd choice listed for simplicity, & because it wouldn't matter under realistic conditions anyway, & because in this 3-candidate race they have no reason to vote a 2nd choice, & because it will matter later when I discuss an _implausible_ eventuality]
If voters vote complete & sincere rankings, Clinton wins by Condorcet & by Copeland. The difference between those 2 methods isn't tested here, since there's no circular tie to solve. Clinton beats Dole 60-40, & Clinton beats Nader 65-35.
Now say the Dole voters "truncate", or "bullet-vote", and don't rank Clinton. This could be done strategically, but will be quite commonly done without any strategic intentions. Here are the resulting rankings:
40%: Dole 25%: Clinton 35%: Nader, Clinton
Now we have a "circular tie", in which the Dole voters have allowed Nader to beat Clinton 35-25. The other pairwise results are as above. Nader beats Clinton beats Dole beats Nader. A circular tie.
Alright then who's least beaten by Condorcet's rule? Well the Dole voters can't do anything about the fact that Dole has a majority against him, a 60-40 majority. Nore can the Dole voters' truncation change the fact that there is no majority against Clinton. Clinton only has the smaller of the 2 extremes against him, 35%. Dole has 60% against him, and Nader has 40% against him. Clinton wins. The Condorcet winner who'd beat each one of the others in separate 1-on-1 elections wins.
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Now, you may at some point hear someone express concerns about "order-reversal", so let's try it in this example. Let's say the Dole voters attempt order-reversal strategy, in order to make Clinton very beaten, hoping that will help Dole:
40%: Dole, Nader 25%: Clinton 35%: Nader, Clinton
This time the Dole voters have caused Clinton to be beaten 75-25. As before, the Dole voters can't do anything about the fact that Dole has a majority against him, a 60% majority.
But another thing the Dole voters can't do anything about is the fact that Nader _doesn't_ have a majority against him. The Dole voters, since they don't constitute a majority (Dole couldn't lose if they did) don't have the power, on their own, to make someone be beaten by a majority. They only did it to Clinton with the help of the Nader voters. But no one's helping them do it to Nader.
Therefore, there's not a thing the Dole voters can do to keep Nader from winning. Well there's 1 thing they can do: They can avoid the fruitless risky order-reversal attempt.
Notice that all it took to punish the order-reversal, to make it impossible for it to succeed, was for the Clinton voters to not vote a 2nd choice, or at least to not vote for Dole. But it wasn't even necessary for the Clinton voters to know which side would be the big side with the capability of trying order-reversal-- merely not voting a 2nd choice completely thwarts any order-reversal attempt.
So then, that's the defensive strategy against order-reversal: Don't vote for the candidate of the likely order-reverser. In general, don't vote for anyone you like less than the likely Condorcet winner. In a 3-candidate race, there's no reason for the Clinton voters to vote a 2nd choice anyway. In a larger election, more candidates, it could be uncertain who's Condorcet winner, but all voters have access to the same strategic information, and the Dole voters know that. So the mere fact that other voters even _might_ expect the possibility of order-reversal, and vote accordingly, is enough to deter the order- reversal.
I re-emphasize that this won't happen anyway. Bruce & I have agreed that the devious strategy of order-reversal won't be tried in a public election on a scale sufficient to change the election result.
***
Sorry about going into such detail about something that won't happen.
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Now, what would Copeland do in the 2 above cases, where the Dole voters truncated, and where they order-reversed?
Well, first of all, Copeland is always completely indecisive in a 3-candidate race, and relies completely on a tie-breaker. Bruce proposes, in his Regular-Champion method, that Condorcet use Plurality as its tie-breaker. So what would happen?
In both circular tie examples, Regular Champion's Plurality tie-breaker would pick Dole. If we want something better than Plurality, the above example would suggest that we need somethng better than Copeland or Regular-Champion, to paraphrase something that was recently said to you.
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Our goal in single-winner reform can be summarized by saying that we want to get rid of the need for defensive strategy to the greatest extent possible.
A group of voters consisting of a full majority of all the voters has the power to make happen whatever they want to. Easy enough if they all vote the same candidate in 1st place, but not so easy if what they all agree on is that they want to defeat a certain candidate. They can always do it, always get what they all agree on wanting, but with most methods, including Copeland, that will often require "defensive strategy": They'll need to voter other than sincerely.
I define "defensive strategy", then, as the need for a full-majority group of voters to vote other than sincerely to get a result that they all want.
The need for defensive strategy is to be minimized, and is to be completely gotten rid of when possible.
The above 2 paragaraphs summarize what we want in a single-winner method. We could call that the "Defensive Strategy Standard", or we could call it the "Generalized Majority Standard". I'm calling it both.
That standard is a general statement of what we'd all like. It isn't the kind of simple yes/no test to apply to a method, the kind of thing mathematicians like, so I'm calling it a standard, rather than a criterion. But that standard still has a definite meaning, and specifics can be added.
For instance, since, as I showed, Condorcet won't ever elect someone with a majority against him under plausible conditions where the result matters, that means that Condorcet is completely free of defensive strategy need under those conditions.
I showed, in the 3-candidate example, how easily it is to thwart order-reversal, in the highly implausible scenario where it's a possibility. The fact is that, in Condorcet, a group consisting of a majority not only has the power to make someone have a majority against him, but also has the power to make anyone else _not_ have a majority against them (simply by not helping vote anyone over him). This means that, simply by voting a short ranking, a ranking that doesn't include a particular candidate, a full majority who rank someone over him have the power to ensure that he can't win.
Summarizing that paragraph, a full majority have the power, in Condorcet, to ensure the defeat of any candidate without using any strategy other than a short ranking. They don't need to use the insincere voting strategies of voting anyone else equal to or over their favorite. No need for defensive strategy involving order-reversal or insincerely ranking 2 candidates equal.
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Now, because the real world isn't always as neat as voting-system reform advocates would like it to be, I have to say that, if there are lots of candidates, and if the cheating voters have impossibly accurate & complete predictive informtion, and are very improbably sophisticated additionally, then they could contrive to create a circular tie among the candidates whom they're voting over the Condorcet winner, and, if they're impossibly lucky & well- informed, could create a combination of their votes with the votes of those canddiates' supporters that would cause all those candidates to be have majorities against them.
Forget it. It's impossible. But a mathematician would object that the fact that that can be mentioned, even in principle, should prevent me from saying that Condorcet guarantees that it's _never_ necessary for a group consisting of a full majority to use use order-reversal or insincerely rank candidates equal in order to get a result that they all want. Sorry, mathematicians, I'm saying it anyway.
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Aside from that, it's also true that adding a simple refinement to Condorcet would make the impossible-in-practice offensive strategy in the previous paragraph impossible-in-principle too:
When A beats B beat C beats A, that's called a circular tie if these are the only alternatives, or the ones that beat all the others. But in general, it's called a "cycle". It's possible for one element of a cycle to be a cycle. In other words, it's possible for a cycle to be an element of a cycle. Such a cycle that is an element of another cycle can be called a "subcycle".
So we simply add this rule: Subcyles shall be solved by Condorcet's rule before solving a cycle that they're part of. The winne in the subcycle shall take that subcycle's place in the cycle that the subcycle is part of.
In other words, we start with by solving the highest-order subcycles by Condorcet's rule. We than replace that subcycle by its winner, in the cycle of which the subcycle was an element.
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Now someone might object that that's too complicated to propose to the public. Here are 3 answers to that:
1. It won't be needed anyway, since the kind of offensive strategy that it would make impossible-in-principle is already impossible-in-practice.
2. If some voters were sophisiticated enough to attempt order-reversal, then others would be sophisticated enough to know about it to, and would be open to suggestions on how to thwart it, and would be interested enough to listen to the subcycle rule.
3. The subcycle rule isn't really complicated, and its wording can probably be improved.
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One last thing about order-reversal, it should be obvious that it the Dole voters, for instance were organized to order-referse, this would take lots of public communication about it, and it would be quite impossible to keep this information from the other voters, who could easily use easy non-devious, non-insincere counermeasure against it (not ranking Dole). So the reversal would backfire & elect Nader.
And even aside from everything said so far about order-reversal, the fact that it could only work if its victims voted for the perpeterators' candidate makes it a particularly dastardly betrayal. If it were attempted even once by Republican voters, whether it succeeded or not (& I've shown why it wouldn't), the intended victims of the order-reversal would never again rank a Republican candidate.
All in all, then, order-reversal is not a problem in Condorcet, though I readily admit that it could be a problem in Copeland.
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Sorry about the amount of detail, but that's what it takes when detailed criticism is possible. I had to cover the topic so as not to be accused of leaving something out, in the Condorcet vs Copeland debate.
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Mike Ossipoff
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