Example with contrary half preference votes

Hugh R. Tobin htobin at ccom.net
Sat Jul 13 11:04:40 PDT 1996

Mike Ossipoff wrote:
> This example for margins vs votes-against is the same one that
> I just used for the compulsory falsification issue:
> Sincere preferences:
> 46%: Dole, Clinton, Nader
> 20%: Clinton
> 34%: Nader, Clinton, Dole
> Dole voters truncate:
> 46%: Dole
> 20%: Clinton
> 34%: Nader, Clinton
> If we use votes-against, as specified by the rule for
> Condorcet's method, then Clinton wins. The truncation
> by Dole voters can't change the fact that Dole has a majority
> against him, nor can it change the fact that Clinton doesn't
> have a majority against him.
> If we go, instead, by margins of defeat, Dole wins, meaning
> that the truncation by Dole voters has taken the victory from
> the Condorcet winner & given it to the candidate of the
> truncators. The wishes of the majority that indicated that
> they'd rather have Clinton than Dole is violated. GMC &
> LO2E-1 are violated. The Nader voters would have better optimized
> their outcome if they'd insincerely voted Clinton in 1st place.
> That's just what we don't want anyone to feel compelled to do.
> (In a pairwise comparison, margin of A's defeat by B is
> gotten by subtracting the number of voters who voted A over
> B from the number who voted B over A).
> Mike
> --

But you are assuming that the Dole voters actually prefer Clinton to 
Nader, which is wholly implausible given how they voted.  (It is hardly 
surprising to see the "Condorcet winner" lose when a block of his 
supposed supporters in a pairwise contest comprising nearly half the 
voting public somehow fails to show up for that contest!) I think we 
agree the Dole voters would not use truncation as an offensive strategy, 
because it is such a weak device.  So the only plausible interpretation 
is that they really do not care between Clinton and Nader.  Therefore 
Clinton is not Condorcet winner, and a Dole victory using "margins of 
defeat" is not a sign of any defect in that system.  Note that if 
half-votes are optional, the Dole voters will choose that option if they 
understand the tiebreak system, because that is how they give their 
candidate the best chance to win, as your example shows.  Then if the 
Clinton voters opt-out of half-votes, Nader will win, but the Clinton 
voters would not do that if they were sincerely indifferent, because 
Clinton's own chances to win would suffer, for no possible gain (the 
Clinton voters don't know how everyone else is voting).  Clinton will win 
with the votes in your example only if half-votes are prohibited or if 
the voters are confused about the significance of choosing half-votes.  
If you agree that the truncating voter should be able to choose half 
votes, and should be educated as to how they work, then I don't think you 
can expect Clinton to win in your example.

However, I think the question you were responding to was about the 
difference between my proposal and "margins-of-defeat", not the 
difference between counting equal rankings as zero and "margins of 
defeat".  Even if that wasn't the question and if everyone is at best 
sincerely indifferent to my proposal, here's my answer.
 My proposal was:

" In Smith//Condorcet, I suggest the tiebreak based on who is
"least beaten" should count equal rankings or non-rankings under
 the following principle:

In each pairwise contest between X and Y, count as 1/2 vote for X and
1/2 vote for Y an equal ranking of X with Y by a voter, if that voter
ranked all other members of the Smith set ahead of X and Y.  Otherwise
count the ranking as 0 votes for each.  (All non-rankings count as equal
last rankings)"

The answer is that when all equal rankings are at the bottom of voters' 
ballots, there is no difference between my proposal and "margins of 
defeat", because all equal rankings are counted as half votes (in that 
situation, using "margins of defeat" accurately reflects the expressed 
intentions of the voters).  The difference arises when voters rank two or 
more candidates equally and rank other candidates lower, and one of those 
lower-ranked candidates gets into the Smith set. In that case counting 
half-votes could be inconsistent with the preferences expressed by the 
voter's ballot, so my proposal does not count them. (One could give the 
voter an option as to whether the half-votes should count if the Smith 
set includes candidates that she ranked both above and below the 
equally-ranked candidates, but that would be a bit complicated to 
explain). Therefore, a candidate who was equally ranked with another by 
enough voters, above another candidate in the Smith set, could be 
"least-beaten" under my proposal even though her loss to that 
equally-ranked candidate was by a greater margin than the loss of another 
candidate in the Smith set.  Sorry, I don't have an example at hand, but 
will work one up if I have time.

-- Hugh Tobin

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