# [EM] Replies to Saumur

Mike Ossipoff dfb at bbs.cruzio.com
Mon Mar 4 01:57:47 PST 1996

```Lucien Saumur writes:
>
> In an article, dfb at bbs.cruzio.com (Mike Ossipoff)  writes:
>
> >Lucien Saumur writes:
> >
>
> >>           The voters who produce a circular tie are like
> >> the car buyer who walk into a car dealership to buy a car.
> >> that he prefer a blue car to a red  and when told that
> >> there is a blue car in stock for him, he says that he
> >> prefers a white car to a blue car. Finally, when he is then
> >> told that there is a white car in stock for him, he says
> >> that he prefers a red car to a white car.
> >
> >No, not necessarily. As I said, truncation--the voting of a short
> >ranking, is quite common in rank-balloting elections, and can easily
> >cause a circular tie, even when there's a Condorcet winne (candidate
> >who'd beat each one of the others in separate 2-way races).
>
>           I do not see how short ranking can cause a
> circular tie. Short ranking means that a voter is saying:

Here's how:

In the Clinton, Buchanan, Nader example I gave, the _sincere_
preference orderings are:

12.5%: Clinton, Nader, Buchanan (assuming equal split for
2nd choices among Clinton voters)

Say the Buchanan voters don't vote a 2nd choice, for whatever reason.
Then we have 25% ranking Clinton over Nader, & 35% ranking Nader over
Clinton. So Nader beats Clinton 35-25.

Similarly, Buchan beats Nader 52.5-47.5, & Clinton beats Buchanan
60-40. That's a circular tie, resulting from truncation. I didn't
say _everyone_ would truncate--I spoke of the undesirability of
truncation by the Buchanan voters stealing victory for Buchanan
from the Condorcet winner.

In Random-Solution, there's only 1 chance in 3 that this truncation
by the Buchanan voters will produce a result worse for them than the Clinton
victory that would have happened without the trunction. That isn't
acceptable. With Condorcet's method it's impossible for truncation
to elect a majority-rejected candidate, stealing the election from
a Condorcet winner. The fact that a full majority rank Clinton over
Buchanan makes it impossible for Buchanan to win unless _every_
candidate has another candidate ranked over him by a full majority,
something that would require either large-scale order-reversal, or
what we both agree is a genuinely ambiguous, chaotic, & indecisive
situation.

> "If my preferred candidate(s) is (are) not also preferred,
> to the other candidates, by the voters, then I accept
> whatever other candidate the other voters will choose. If

But that abandonment of the compromise can, as I showed, make
the election result into a circular tie, as it would be if there
had never been a Condorcet winner. Except that there is one, who
may or may not get elected, depending on which circular tie solution
we're using.

every voter short-ranks and votes for only one candidate,
> then this electorate will have converted the preferential
> ballot election into a FPTP election. The FPTP winner is

If every voter short-ranks, that's a situation that I haven't
discussed, and which we needn't be concerned about. If the people
who really need the compromise don't rank him, then there's really
nothing that any method can do for them.

> also the Condorcet winner since he has beaten every other
> candidate, in a pairwise contest.

Oh no, the winner if everyone just votes for their 1st choice will
be, in my example, Buchanan, who is _not_ the Condorcet winner. Clinton
is Condorcet winner in that example.

But yes, if everyone only voted for their 1st choice, Buchanan

would beat everyone in pairwise comparisons, and would win, in Condorcet's
method, by virtue of that.

Although, with everyone sincerely ranking all the candidates, the Condorcet
winner will beat everyone, we can't call the person who beats everyone
the Condorcet winner, since bullet-voting by everyone, as you pointed out,
can make Buchanan beat everyone in pairwise comparisons.

With everyone bullet-voting, Buchanan would be winner by Condorcet's
method, but the word "Condorcet winner" is reserved for the candidate
who'd beat each one of the others in separate pairwise elections, if
people voted sincerely (and they'd have no reason not to in a 2-way
race).

>
> __________________________________________
>           aa447 at FreeNet.Carleton.CA
>           http://www.igs.net/~lsaumur/
> .-
>

--

```