# [EM] Condorcet cyclic drop rule

MIKE OSSIPOFF nkklrp at hotmail.com
Thu Mar 29 00:08:13 PST 2001

```Tom wrote:

>#1 Example ballots: AC=5, BA=4, CB=3
>
>  Pair elections:
>A:B=5:7   B/A (7) - weakest
>B:C=4:8   C/B (8)
>A:C=9:3   A/C (9)
>
>  Dropping B/A counteracts only 7 voters' preference, compared with 8 or 9.
>The result is A>C>B, and A wins.
>
>  However if some "A" voters bullet vote:
>#2 Example ballots: AC=3, A=2, BA=4, CB=3
>
>  Pair elections:
>A:B=5:7  B/A (7)
>B:C=4:6  C/B (6) - weakest
>A:C=9:3  A/C (9)
>
>Dropping C/B counteracts 6 voters' preference, compared with 7 or 9.
>The result is B>A>C, and B wins.
>
>It is strange - A supporters might dislike B and C equally, but strategic
>voting for C second helps while A loses if supporters bullet vote instead!

Blake discussed that, and I answered it. I'll find it in the

But I'll state some of the answers here: It's only true in
0-info elections where there's a natural circular tie. It isn't
about a majority being forced to defensively order-reverse in order
to defeat a lesser-evil. True indifference is the exception.

You know, one can come up with any number of examples showing something
that doesn't make sense, some paradox of rank balloting, for instance.
But we choose a voting system because it meets some particular criteria
that we consider more important than others. Show all the Condorcet
paradoxes you want, but I like it because it does so well in
getting rid of the lesser-of-2-evils problem and in protecting majority
rule. If you don't value those standards, but value some other standards
instead, then of course you may well prefer another method. And you
won't be wrong. Your standards aren't wrong. Standards aren't wrong or
right. They're a relativist sort of a thing.

>
>Ranking is truly a bizarre world!

I'll tell you something else: With Condorcet or IRV, if you show
up and add to the count a ballot that votes A over B, that can
change the winner from A to B.

That can happen with any rank method except for Borda, a method that
has some fatal problems in political elections.

If you don't like any paradox, then stick with Approval.

>
>Random determination to break a cycle would seem a safer bet to me to
>discourage insincere voting in lower rankings.

We can also discourage insincere voting by Random Ballot, or by
Random Candidate (which would eliminate all voting).

>
>I would guess cycles come from three types of sources:
>1. Irrationally or thoughtlessly lower ranking.

I've never understood your "irrational or thoughtless lower rankings".
Are you talking about someone who makes out his lower rankings
randomly, when he doesn't have any preferences between those
candidates? Blake has shown that doing that can be advantageous
in Condorcet, in a 0-info election, when there's a natural circular tie.
As I was saying, I answered him at the time, and it's in the archives,
and I'll find it & re-post it. A brief answer was given above in
this message.

>2. Insincere strategic lower rankings.

Offensive order-reversal (aka "burying"). Possible, but risky, with
Condorcet.

>3. Voters in different coalitions may use different fundamental criteria
>for
>judging candidate. (Imagine 3 candidates {A,B,C} and 3 qualities/issues
>{X,Y,Z}. Each candidate has a different set of 2 of the 3 qualities - A has
>X much and Y some, B has Y much and Z some, C has Z much and X some. Then
>voter come in 3 groups: one likes Y much and X some (vote AB?); one likes Z
>much and Y some (vote BC?); one likes X much and Z some (vote CA?). This
>could cause a ranking cycle if no coalition group has a majority.)

Sure, natural circular ties are possible. It's even been pointed out
that one particular person could have nontransitive pairwise prefereces
when there are several attributes to compare by. An old Scientific
American article showed how someone could prefer apple pie to
chocolate pie, chocolate pie to pumpkin pie, and pumpkin pie to
Apple pie.

Mike Ossipoff

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