[Election-Methods] Ballots with cycles

[Juho]

Thanks. I missed the part of breaking the ballot into pieces already  
before counting it.

I know one example where at least people claimed that one person  
monitoring the elections in a small village, after watching all the  
voters vote, after the day had almost accurate results on how many  
votes each candidate got (there were numerous candidates). I think  
with this kind of good understanding of the local people one could  
guess whose ballot some ballot is if one would see the detailed  
content of the ranking (or rating) based more complex ballots.

One approach to fixing this is to increase the size of the lowest  
level vote counting areas, e.g. from minimum size of 50 to minimum  
size o 500. This may depend also on the number of candidates.

One aspect that may reduce the problems is that people may rank only  
a limited set of the candidates. But of course they are not  
guaranteed to do so. One rather radical way to make the votes more  
unidentifiable would be to simply allow the voters to mark only n  
candidates, or use only m ranking categories for all of them.

A bad example case might be one where I vote:  
MyBrother>MyFriend>MyNeighbour>MyPartyMember1>MyPartyMember2. If some  
of the people close to me and my friends would be one of the vote  
counters he/she could with reasonable certainty check that all in the  
"team of friends" voted as expected.

Another bad example is to ask someone to vote  
WeirdCandidate1>WeirdCandidate2>MrX>... and another one  
WeirdCandidate7>WeirdCandidate6>MrX>... This would allow MrX to buy  
votes or coerce voters. The weird candidates are marked just to make  
the ballots recognizable (they have no chances of winning the race).  
They could as well be at the end of the ballot (to avoid the risk of  
them getting elected).

So, if one wants to avoid all this one could mandate (not only allow)  
the voters (or the voting machine) to cut their votes into smaller  
two-candidate relationships already before dropping the vote into the  
ballot box. On the other hand one should still make sure that  
everyone casts only one vote and doesn't e.g. drop two A>B ballot  
fragments into the box. Because of all the complexity this could  
maybe be best done by a machine. The voter would just mark ordinary  
preferences and then the machine would cut the vote into small vote  
fragments and drop them into the box. And if this is done by the  
machine there would again be no compelling need to allow circular  
votes (hard enough to guess the original linear votes from the  
fragments). One could in this case as well allow only linear votes  
but still break them into intraceable fragments.

Juho


On Mar 6, 2008, at 2:17 , 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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