[Election-Methods] Ballots with cycles

[Dave Ketchum]

Let's look at Condorcet:

Voter ranks as many candidates as wished, assigning each of them a rank.

Counter records in an array with one row and one column for each candidate.
      For each pair of ranked candidates, calling the higher ranked A, and 
the other B, count in row A, column B.
      For each pair of ranked candidate A and unranked candidate B, count 
in row A, column B.

The array contains nothing but the total counts for all the ballots in the 
precinct.

The ballots have no further purpose to serve.

Does not seem possible for your proposal to make the ballots less 
identifiable.

Does not seem practical for your additions to be useful:
      They seem more difficult to use than normal.
      If they, somehow, give a voter extra power, seems like they should 
be forbidden.

DWK

On Wed, 5 Mar 2008 19:17:06 -0500 Andrew Myers wrote:
> 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
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  Dave Ketchum   108 Halstead Ave, Owego, NY  13827-1708   607-687-5026
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