[Election-Methods] Ballots with cycles

[Andrew Myers]

Juho wrote:
>
> 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 votes 
> would be simpler).)
Juho,

Thanks for your thoughts on this.

The reason to have it is that you can take a ballot that is expressed as 
ordinary rankings and decompose it into a set of individual preference 
relationships, each of which does not reveal much information about the 
voter. The various preferences are still summable, but preferences 
coming from different voters can be mixed together, preserving their 
privacy. This addresses a vulnerability sometimes called the "Italian 
attack" or "Sicilian attack", legendarily associated with some elections 
in that region (I have no actual evidence that this really happened!), 
in which voters could be identified by the precise rankings used in 
their ballots, dictated by party bosses. With N alternatives, the N! 
possible orderings can uniquely identify many voters.

The concern is that a voter might be able to inject a set of preferences 
into the system that do not correspond to any numeric ranking, if they 
control the software is that generates the preference relationships. So 
the question is whether there is a scenario in which a voter doing this 
is able to swing an election that cannot be swung by a voter who only 
generates transitive orderings.

-- Andrew