Example with contrary half preference votes

Mike Ossipoff dfb at bbs.cruzio.com
Mon Jul 15 00:55:21 PDT 1996

Hugh R. Tobin writes:
> Mike Ossipoff wrote:

[I'm falling farther & farther behind in replying to Tobin's
letters. But I will catch up. In the meantime, I'll be posting
a few letters that each reply to a few topics. Then I'll go over
the unanswered letters, and list other statements to which I'll
reply in an additional letter. But, also, I'm directly replying
to some letters, like this one. After posting this direct reply,
I'll post a letter replying to a few statements, which isn't
a direct reply to any particular letter.]

> > 
> > 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 

Not necessarily. Some people might still refuse to express a
preference, even though it can't profit them, because they
don't understand that it won't help them. I gave the example
of a guy who did that in an organizational election.

But, more important, truncation (by which I mean voting a short
ranking that doesn't express all of one's preferences) will be
quite common in public rank-balloting elections, just as it
has been in every rank-balloting election I've participated
in. So you're in error if you're saying that it won't happen.
It will happen regardless of what count method is used.

You might say that the Dole voters, in our example, aren't going
to truncate due to laziness, when there are only 3 candidates.
Sure, but remember that there won't really be just 3 candidates
when rank-balloting encourages more people to run.

Besides, as I've already pointed out, there are other reasons
for truncation, other than strategic intent & lazinesss. There's
principle: Dole voters might feel that Clinton is so far below their
standards that they refuse to vote for him on principle. Similar,
but not exactly the same, they might refuse to vote for him to
send a message, to make a point, to make a statement.

The point is that truncation will happen a lot, just as it
always has in all of the rank-balloting elections that I've
participated in.

> surprising to see the "Condorcet winner" lose when a block of his 
> supposed supporters in a pairwise contest comprising nearly half the 

I don't call them "supporters" if they refuse to rank him, even
if they prefer him to Nader.

> 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 

No. I answered that in a previous paragraph in this letter. I've
also answered it in previous letters.

> Clinton is not Condorcet winner, and a Dole victory using "margins of 

In my example, Clinton is most emphatically Condorcet winner,
because the sincere rankings were explicitly stated, before
the actual voted rankings.

> 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 

No they won't, because in reality Dole voters surely like Clinton
better than Nader, and we're talking about an example where that
is the case. In that case, opting for the falsification would
most likely backfire by electing Nader. It wouldn't succeed, and
it would result in an oucome worse for the perpetrators than what
would have happened had they not falsified.

> 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's chances to win would suffer from Dole voters' falsification
anyway. If it's known that Clinton voters aren't voting a 2nd
choice, then no one will attempt falsification strategy, since
it can't possibly work. Therefore Clinton will win. Clinton's
chances to win haven't suffered, they've been protected.

> 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.  

In my example the Clinton voters didn't vote a 2nd choice, and
so falsification by the Dole voters could never elect Dole. If,
as specified in the example, the Dole voters prefer Clinton to
Nader, then the falsification backfires reliably. Clinton wins because
falsification wouldn't be attempted if voters know what they're
doing. Clinton wins without false half-votes being prohibited.
So your statement in the above quoted paragraph isn't correct.

> 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.

Clinton would win.

> 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 

Saumur had asked about the difference between margins & votes-against,
and I compared margins' results to my version of votes-against.

> 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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