[EM] Two Condorcet Winners?

Adam Tarr atarr at purdue.edu
Fri Aug 23 22:58:03 PDT 2002

>1) Why is it that important that "truncation won't steal the election
>from a majority-supported CW"?

The reason it is important is because it makes the CW a stable winner, and 
therefore resistant to strategic manipulation.  Truncation is a very 
natural thing for the voter to do, especially since they already vote a 
single candidate in current elections.  If a candidate encourages his or 
her supporters to truncate )or "bullet vote" or whatever you want to call 
it) this will not be seen as an underhanded strategic move.  And yet, this 
sort of subtle manipulation can cause the Condorcet winner to lose the 

So winning votes has a big advantage over margins (or relative margins; 
they seem very similar strategically), since voters will NOT have the 
incentive to truncate their ballots.  They will get the same results, or 
better results, if they fully express their preferences.  In order to 
strategically manipulate the election in a winning votes system, voters 
have to actually switch the order of their lower choices.  This works in 
margins-based Condorcet voting as well.

I've heard two arguments to refute my above point:

1)  "There's no inherent value in the Condorcet winner."  This is Don 
Davidson's argument (and the argument of other IRV advocates).  Obviously 
if you think this, then the whole margins vs. winning votes debate is 
completely moot anyway, so this point is really irrelevant to our 
discussion.  I think both of us _do_ value a sincere Condorcet winner.

2)  "There is no point in being resistant to truncation, since the voters 
can just order reverse anyway."  It is true that order-reversal works in 
winning votes -- no real voting system is totally strategy free.  But I 
think that realistically, it would be dramatically harder to convince 
voters to reverse preferences than it would be to convince voters to only 
vote their favorite.  Blake likes to argue that voters will take any 
strategy available to them, but real-world examples (USA 2000, France 2002) 
have clearly (in my mind) shown that voters will take a tack fairly near 
their natural preferences most of the time.  If you make it hard for voters 
to strategically manipulate results, the chance that they will do it (en 
masse) is much smaller.

Large-scale order reversal would probably require a large, public campaign 
that clearly laid out the reasons why voters should vote for a candidate 
they don't like.  The opposition would pick up on this and could counter it 
fairly easily.  It's perhaps worth noting that the counter to order 
reversal is less drastic in winning votes methods as well.  But my argument 
is that it wouldn't even come to that: the lengths one needs to go to to 
vote strategically in winning votes methods would probably render strategic 
voting a non-issue.

>2) Is it an incentive to tell people "go ahead you can truncate, it will
>not change the winner"?

No, rather the incentive is, "go ahead and vote your full true preferences, 
it can only help you".  Margins methods say "truncate, and hide your true 
preferences (in certain cases), because this will give you a better 
result".  Winning votes methods give us less strategy, because they are 
more likely to find the sincere Condorcet winner.  It's win-win.

>3) Is it an incentive to the people to give their real sincere

Yes, in a sense.  I'd much rather have a voting system where expressing 
your full preferences can give you more power, as oppose to a system where 
bullet voting and hiding true preferences can distort the results.

>     I imagine you could say to the people "vote for what you really
>like! Others have no strategical mean to truncate their real preferences 
>in order to steal a CW from you"?  But still, you cannot assure voters 
>that strategy is removed when there is no CW,

True, I can never assure voters that there is no strategy.  But what I can 
assure them is that they will not hurt themselves by voting their full 
preferences.  That is a comfort to me.

>and in addition you cannot ensure voters that an opponent could not steal 
>your CW. He/she could add artificial preferences (ABDEF) instead of voting 
>sincerely (AB) in order to artificially sink the CW (C) and put it into a cycle
>where C could loose.

True again.  Of course this is also true in margins, so it does nothing to 
advance one method over the other.  And again, I think the scenario is 
pretty unlikely.

>4) Thus, isn't the expression of sincere preferences aimed to by using
>winning-votes dependent on having a CW

No, for the reason I just stated.  Winning votes removes the incentive to 
truncate your ballot to manipulate the results.

>and voters having no sincerely truncated
>ranking preferences from the start?

No... why would it depend on that?  Winning votes methods ensure that you 
can never hurt yourself by writing out your lower preferences.  If you have 
no preferences to write, then you still can't be hurt by them...

>5) What do you prefer, a "good enough" winner obtained from a set of
>votes containing an additional incentive toward sincerity or the fairest 
>obtained from a "sincere enough" set of votes?

Gosh, if I had to choose, I'd probably that the latter.  Of course, in my 
opinion, winning votes gives me the fairest winner with the most sincere 
votes.  I don't see how you could argue that the insincere ballots produced 
by a margins method will somehow smoke out the fairest winner more 

Perhaps you can come up with an example of some manipulation caused by 
voting full preferences in winning votes methods (even writing that sounds 
like a contradiction) while margins would get the better results in that 
election.  Meanwhile, I will provide my standard example, which happens to 
illustrate how easily margins methods can be manipulated by the sort of 
truncation that would be easy to talk the voters into.

Sincere preferences are as follows

49: George>Al>Ralph
12: Al>George>Ralph
12: Al>Ralph>George
27: Ralph>Al>George

Al is the Condorcet winner (beating George 51-49 and Ralph 73-27).  Now, 
all the George voters have to do is vote for only George, which doesn't 
strike me as hard to talk them into, and George will win the election.  In 
other words, voting their second place choice (Al) hurt them, and not 
voting that choice allows them to defeat the sincere Condorcet winner.  In 
a winning votes method, Al wins the election either way.


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