As has ofen happened before, I neglected to write down the subject of these postings, and so I'm guessing when I title this one. I hope it isn't too different from the original subject title.
James--
I'd said:
Each Approval election, by its reported vote totals, gives
information for subsequent Approval strategy. If Nader outpolls the Republican, then Nader-preferrers will know that they needn't vote for the Democrat in subsequent elections.
You replied:
Okay, this is an interesting point, but we need to generalize it a bit to make it more widely applicable.
I reply:
No, we don't really need to, but of course it's always good when we can generalize something and make it more widely applicable.
You contilnued:
So, if your first choice is polling comfortably ahead of your third choice, there is no need to approve your second choice, right? Or, if your Nth choice is polling comfortably ahead of your (N+2)th choice, there is no need to vote for your (N+1)th choice. So far so good, but this is a special case and only takes us so far...
I reply:
It takes us far enough that if there's a widely recognized "greater-evil", and your favorite outpolls him, then you don't need to vote for a lesser-evil in order to beat hisi party next time.
You continued:
Approval quickly homes in on the voter median, and then stays there.
I feel that more information is needed to support this claim.
I reply:
That claim is a wording of what Myerson & Weber demonstrated in their article in which they introduced Myerson-Weber equiilbrium and then applied it to some methods, including Approval, Pluralilty and a few others.
But, just briefly, say Favorite is the voter-median candidate. Say the media have been hammering home the message that Sleazy is the voter-median candidate whom we need as a compromise lesser-evil., to beat some greater evil named Worst. So the Favorite-preferrers vote for Sleazy. Everyone who is in the Favorite direction from Sleazy and prefers someone else whom they're closer to will vote for Sleazy, because we're assuming that they all believe that Sleazy is the voter median candidate, the only one who can get a majority against Worst. With all those people voting for Sleazy but not for Worst, Sleazy beats Worst and wins.
But they also voted for their favorites. In fact, in Approval, under any plausible conditions, when you vote for some lesser-evil, you should also vote for everyone whom you like better. That means that all those voters who reluctantly voted for Sleazy are going to also vote for everyone between them and Sleazy.
Half of the voters are in the non-Sleazy direction from Favorite, since s/he's the voter median candidate. When those people vote for Sleazy, they also vote for Favorite, because Favorite is between them and Sleazy. Favorite will get votes from a majority of the voters. Worst won't. Favorite will outpoll Worst. In the next election, those voters will know that they don't need to vote for Sleazy, or his party, or anyone like him in order to beat Worst, his party, or someone like him.
They don't vote for Sleazy. But of course, though Favorite outpolls Worst, s/he hasn't outpolled Sleazy yet. And so maybe there could be some candidate betwen Sleazy & Favorite who emerges as the next lesser-evil due to his/her compromise votes. So, conceivably it could be necessary for the same thing to happen again so that people will find that they don't need that next compromise either. But before long, it will be evident that no one has any need to vote for anyone whom they like less than Favorite's party. Since we're talking about a series of elections in which the candidates might be different each time, it's better to refer to parties instead of candidates, though Nader has run in several consecutive presidential elections.
In practice, though, in our political system, there's really just one gereater evil and one lesser evil: The Republican and the Democrat. Because it's (mis-) perceived as a 2-party contest with just 2 winnable candidates, the Democrat & the Republican. So, in practice, there will only be one Approval election in which a lesser-evil is misperceived to be necessary. That's why I said that Approval will home in on the voter median candidate in the 2nd Approval election.
Someone asked me if I was talking about a 2-balloting method, when I referred to the 2nd Approval election. No. I meant the next election, the next presidential election, 4 years later. Though these methods are good for all single-winner elections, we usually discuss them in terms of the important presidential election.
But I refer you to Myerson's & Weber's article. A reference to it can be found in the references section at the end of Robert Weber's article, entitled "Approval Voting", in the Winter '85 issue of
_Journal of Economic Perspecive_ I'm not entirely sure whether it's "perpective" or "perspectives", but I believe that it's probably the former.
The reference will be to an article whose title refers to a new kind of voting equilibrium. As I said, the authors are Roger Myerson & Robert Weber.
You continued:
Approval
Condorcet goes directly to the voter median in its 1st election.
& CR do so in thei r 2nd election. That's the price of simplicity andeasy
proposability.
You don't seem to be taking into account the possibility that the voter median will change from election to election, as the candidates change, the issues in play change, and the electorate itself changes. A lot of major public offices only come up for election every 4-6 years, in which time a lot of the above variables are likely to change. If approval strategy is always based on the previous election, then it may have a tendency to lag too far behind the reality to be totally effective.
I reply:
You're saying that it's impossible to make 100% reliable predictions. But I've told why people will know that they don't have to vote for someone like Sleazy in order to beat someone like Worst. Why they don't need to vote for Sleazy's party (the Democrats) in order to defeat Worst's party (The Republicans). When you say that things might change, sure, anything is possible, but you're grassping at straws.
I'd said:
candidate
Myerson & Weber point out that Approval (and CR) guarantee that if there's a candidate at the voter median position, s/he will be the only
who can win at Myerson-Weber equilibrium.
I don't fully understand the statement that you are making here; I feel that the wording is somewhat ambiguous.
I reply:
When we say that something is "ambiguous", we mean that it can have more than one meaning. When we say that, we need to specify at least two valid interpretations of what we're saying is ambigluous. Did you forget to tell us what two or more meanings you think that the above passage could be interpreted to have?
Which part of it don't you understand?
You continued:
Is this statement not also true of plurality?
No.
In fact, as Myerson & Weber point out, in Plurality, if the media anoint some two parties (pretty much _any_ two parties) as "the two choices", then those 2 parties can win at Myerson Weber equilibrium from now on.
In fact, I claim that that's what's happening now in our political system. The two media-promoted parties are repeatedly winning at Myerson-Weber equilibrium. Ask some progressive lesser-of-2-evils Democrat voter to give evidence for his claim that Nader isn't winnable and we need the Democrats to beat the Republican. The answer will be: "Nader hasn't won." As required by Myerson-Weber equilibrium, the outcome (Nader's failure to outpoll the Republican) doesn't contradict the predictive beliefs that led people to vote as they did.
Actually Myerson's & Weber's definition of their equilibrium is longer than that. It's interesting and elegant, but applies only to point systems such as Plurality, Approval, CR & Borda.
I'd said:
Because critreria and standards are individual, subjective, and relativist, your criteria and standards, and your preference amongfoir
methods aren't wrong. But your statement about where Approval's strategy
information must come from is incorrect. And your proposed classification name
Approval and CR is silly.
You replied:
Which one? "Pseudomajority methods"
I reply:
Yes.
Mike Ossipoff
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