IME Example

[Mike Ossipoff]

My 3-candidate Dole, Clinton, Nader example wouldn't do to demonstrate
IME, because, with just 3 candidates, the only way Nader could be
Condorcet winner, and not in the middle, would be for Nader to have
an outright majority, in which case he couldn't lose if his voters
vote him over the others, in any of the methods we're discussing.

So it's necessary to add another candidate. The candidates are:
Dole, Clinton, Nader, Gandhi.

>From the polls, these candidates are all nearly equal, as far as
anyone can judge. So the Nader voters & Gandhi voters know that
Clinton might lose to Dole without their help. So they vote for
Clinton, to ensure Dole's defeat.

True preferences:

21%: Dole, Clinton, Nader, Gandhi
28%: Clinton, Dole, Nader, Gandhi
25%: Nader, Gandhi, Clinton, Dole
26%: Gandhi, Nader, Clinton, Dole

Say the Dole & Clinton voters truncate:

Actual rankings:

21%: Dole, Clinton
28%: Clinton, Dole
25%: Nader, Gandhi, Clinton
26%: Gandhi, Nader, Clinton

The result is a circular tie in which Gandhi beats Nader beats
Clinton beats Gandhi. 

With Regular-Champion, Clinton wins by having a plurality.
Thus, with Regular-Champion, the Gandhi voters & the Nader
voters gave the election away to Clinton because the
mistakenly believed that they might need Clinton as
a compromsse to beat someone worse.

That can't happen with Condorcet (by which I mean plain Condorcet
or Smith//Condorcet).

In this election Nader wins, having only  26% against him in
a defeat.

In general, a mis-estimate, however widely held, about who's
Condorcet winner, can't elect someone other than the Condorcet
winner when a majority rank the Condorcet winner above him.
In Condorcet's method. You've seen my wording for the
Invulnerabiltiy to Mis-Estimate Criterion (IME). But let
me repeat it here:

An alternative meets IME if & only if:

Even if everyone ranks an alternative, X, which isn't Condorcet
winner, and no-one ranks any alternative that they like less
than X, that can't result in victory for X if there's a Condorcet
winner ranked over X by a majority of the voters.


Mike


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