# [Election-Methods] Ballots with cycles

Juho juho4880 at yahoo.co.uk
Wed Mar 5 09:46:08 PST 2008

```On Mar 5, 2008, at 14:54 , Andrew Myers wrote:

> Suppose that in a Condorcet system, we allow people to submit a
> ballot that has an arbitrary preference relation, so any two
> alternative A and B can have either A<B, A=B, or A>B. There can
> therefore be cycles in the graph of preferences, like A<B<C<A.
>
> One reason why we might want to set up the system this way is that we
> can protect voter privacy better by separating different preferences
> during the tallying process.

I don't think this makes much difference. It is also ok to separate a
regular linear opinion A>B>C to three separate binary preferences
A>B, A>C and B>C. And in both cases the typical way to carry the
results forward from the first place where the votes are locally
counted is in a form of a pairwise matrix, so the ballots can be
packed, sealed and stored locally if needed.

Normally we assume that voters are rational in the sense that they
can set a personal preference order to the candidates. With this
assumption the possibility of giving arbitrary preference relations
is of no use to sincere voters.

> The question is whether this creates new strategic voting
> opportunities. I have not been able to construct a scenario where it
> makes strategic voting more powerful.  Is this worse than burying
> with ordinary ranked ballots?

This makes it a bit easier to intentionally generate a loop among say
three candidates (A,B,C) of the competing party. My vote could be
X>A, X>B, X>C, A>B, B>C, C>A, where X is my own party candidate. If
many X supporters vote systematically this way there is a chance that
the candidates of the competing party will all lose to each others,
and that might make X the winner in some Condorcet methods like
minmax if the race is otherwise very tight between the two parties.

Use of arbitrary preferences is interesting but rather theoretical,
and the changes in the outcome might be marginal (at least in typical
public elections). Any more reasons why it should be allowed?

(In regular public elections also the complexity of the ballots might
be a show stopper.)
(If different ballots have different complexity that might be a risk
to voter privacy (you would cast a complex vote while most other

Juho

> -- Andrew
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