[EM] When Voters Strategize, Approval Voting Elects Condorcet Winners but Condorcet Methods can Elect Condorcet Losers

Abd ul-Rahman Lomax abd at lomaxdesign.com
Tue Jul 17 11:21:52 PDT 2007

It's a little-noticed fact that, in Warren Smith's IEVS simulations, 
which generate sets of voters with simulated utilities, then apply 
various voting methods and strategies, (see rangevoting.org), Range 
Voting, when voters "strategize," is actually beaten by Range with a 
top-two runoff.

Range Voting with "sincere" voters is going to be the best method, 
practically by definition, if voters actually vote their utilities. 
However, it is practically unavoidable that real utilities are 
normalized, at least, and, in discussions on the Range Voting list, 
I've pointed out that there are actually several normalizations that 
cause deviation from true, absolute utility.

So there are discrepancies between true maximized utility and utility 
as found by summing Range Votes.

I have suggested that, under some conditions, Range elections be 
subject to a runoff. In the simulations, this was a top-two runoff, 
but I'm suggesting something slightly different in principle, but 
that in most elections would work out to the same in practice.

Range (and Approval) *usually* discovers the Condorcet winner. 
Because of this, when the Condorcet winner and the Range winner 
differ, *usually* the Condorcet winner will be the Range runner-up.

Because of the obvious majority rule principle that the winner of an 
election should not fail to prevail were a runoff between this winner 
and any other candidate to be held, I'm suggesting that when analysis 
of the Range ballots -- this requires sufficient Range resolution -- 
fails to show majority consent for the winner, a runoff be held.

In Approval, the similar principle would trigger a runoff when there 
is no candidate with majority approval, and, quite possibly, when 
there is more than one.

What these runoffs, properly designed, would do is to cause Range and 
Approval to clearly satisfy the Majority and Condorcet Criteria, thus 
removing a major objection that is commonly raised to them.

Note, however, that "majority failure" occurs in Range under a 
special condition: the presence of a weak preference of a majority in 
the face of a strong preference of a minority. Hold a runoff under 
these conditions, and there is a *very* good possibility that the 
voting pattern will show a shift in outcome. That is, even though the 
original ballot would show, under the conditions described, that a 
candidate is the majority winner, there are three factors weighing in 
favor of the Range winner in the runoff that, except where there has 
been a real failure of the Range method to detect the SU winner -- 
i.e., the special condition I mentioned does not truly apply to the 
absolute utilities, but only to the *appearance* of those utilities 
in the Range ballots -- I expect would normally cause the Range 
winner to prevail. The factors are:

(1) The Range winner supporters are relatively highly motivated to 
turn out and vote for their favorite, and have no special motive to 
switch their vote to the pairwise comparison winner.

(2) The Pairwise winner supporters are, relatively, weakly motivated 
to turn out, so we can expect some shift in voter turnout favoring 
the Range winner.

(3) If the Range utilities fairly reflect the real utilities, the 
Range winner is, by definition, better for society, and these are 
conditions where, once this is known, some will switch their preference.

So this system is stacked against the Preference winner. But if the 
preference is a better indicator of the real situation, that stacking 
will largely be inoperative, the Preference winner has a chance of winning.

In any case, the final decision is made by the electorate, not by 
blind application of the Range method.

And, because usually what I'm proposing would end up being a top two 
runoff from a Range method, we can expect that, besides satisfying 
basic principles of democracy, it will elect, a little more often, 
the true social utility winner, as shown by the simulations.

You can have your Condorcet cake and make the most people happy too!

A Note on How I Came to This:

For quite some time, I've been aware that standard deliberative 
process, through a motion to elect a named individual, and iterated 
amendments, should discover and elect the Condorcet winner; however, 
the debate that is part of standard process also will cause 
preference shifts to take place, as members of the organization adapt 
their personal preferences based on perception of common good. In 
other words, it will also elect the Range winner, if the process is 
followed with sufficient care. (It often isn't worth the time it takes....)

There is no way that any "election method" can truly take the place 
of full deliberative process, which is intelligent, it is not merely 
an amalgamation algorithm, but the two-step method I've proposed is 
probably about as good as we might get with two steps. The second 
step, the runoff, should be relatively rare, based on simulations. 
Good nomination processes, a whole other issue, should make it even more rare.

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