[EM] Geographically proportional ballots

[Kristofer Munsterhjelm]

Juho wrote:
> On Aug 28, 2008, at 11:36 , Kristofer Munsterhjelm wrote:
> 
>>> One more approach to semi-computerized voting. A computer displays 
>>> the personal alternatives and then prints a ballot. This solution 
>>> hides the personalized nature of the ballot and still avoids the 
>>> problem of voter voting for candidates that he/she should not vote.
>>
>> One could augment the semi-computerized voting by making it print all 
>> candidates
> 
> That could be thousands, so maybe a subset in many cases.

Just enough to hide the data. One could print out to the nearest 
candidate that's, say, a tenth of the population away from the voter.

Here I say that a candidate is N voters away from a voter if it's not 
possible to make a compact region that includes both the voter and the 
candidate, yet has fewer than N voters in it. For simplicity, the region 
might be a circle.

>> , but randomly order (last behind all others) the ones that are not 
>> applicable to the districts.
> 
> I guess one would need to know the district (or the person if the 
> candidate lists are personal) to "decipher" the vote in the calculation 
> process. That information could help also the malicious readers. Or did 
> you mean that the random data would be part of the vote but would be 
> just noise since different ballots would cancel the effect of each others.

The latter. The idea is to append a ballot with noise so that a voter 
that votes A > B > C > rest, with the first of the rest being (randomly) 
D cannot be distinguished from a voter somewhat closer to A, B, C, and 
D, voting A > B > C > D > rest, except probabilistically with a 
resolution too low to discern individual voters.

> Voter would have also have to trust that the printed ballot is what it 
> should be.

True, that's a problem, and it's not even possible to know whether the 
printed ballot has some hidden information in it. For instance, the 
voting machine might have been tampered with so that it encodes a 
timestamp (or copy of the first few ranked votes) into the random-last 
votes, encrypted so that it's indistinguishable from the noise a good 
random process would produce.

> The technique that I proposed above would work best with bullet votes 
> (e.g. with open lists). Also short votes (that list only few candidates) 
> are quite ok (some risk if one votes for the most distant candidates in 
> all directions).

Yes; and also large virtual districts.

>> However we look at it, we return to the problem that ranked ballots 
>> can be fingerprinted. The only solution I can see for that is to have 
>> a summable system and add the individual ballot in matrix (or array) 
>> format instead of ballot format. But most PR methods are not summable! 
>> Are there other ways of preventing ranked ballot fingerprinting?
> 
> One could break a Condorcet ballot A>B>C to separate pairwise 
> preferences A>B, A>C and B>C (is this what you meant with the matrix 
> format?). If there are also many other candidates (tied at bottom) one 
> could use e.g. A>*, B>*, C>*, cancel B>A, cancel C>A, cancel C>B. That 
> information could be derived also from a more understandable (= easier 
> for the voter to check) set of opinion fragments A, B, C, A>B, A>C, B>C.

That's what I mean, but not restricted to Condorcet matrices. If you 
want to use the ballot data for any sort of positional system (as well 
as those where the positional scores change over time, like Bucklin), 
you'd use an n*n matrix where candidate[0] is the number of times the 
candidate got first place, candidate[1] is the number of times the 
candidate got second place, and so on. Counting a particular positional 
rule requires only an array (one-dimensional matrix), and so on; but all 
of this is made all that more difficult by that no PR method I know of 
is summable without doing quantization on the ballots (like Forest's 
patch does).

I don't know how to capture that formally - perhaps that I know of no 
summable party-neutral PR method that's responsive, if I understand 
responsivity correctly (if there's a tie in the social order, a single 
vote must always be able to resolve that tie). But even that doesn't 
quite get it, for say that some candidate ranked (n+1)th in the 
quantization method has a tie with another. Then a ballot that ranks 
this candidate first would be accepted and resolve the tie (assuming the 
underlying method is responsive, too).

> IRV ballots are trickier. Raph Frank already mentioned the idea of 
> truncation and combination of this with candidate given preference lists.

An interesting corollary of this is that if the quantization method is 
acceptable, then the "IRV is not summable" complaints can be effectively 
countered. Just apply the patch to IRV and then you can sum up the ballots.

> If you allow me I'd like to advertise trees once more. Trees (= 
> hierarchical open lists) can be seen as very truncated ranked votes. 
> Bullet vote to one candidate is inherited by his/her nearest group and 
> so on. When the tree is formed one can expect all common thinking 
> patterns to get their own branch in the tree. If there are lots of 
> people who are green and also somewhat right wing and also a little bit 
> feminist there would probably be such a branch in the tree with few 
> candidates to choose from.
> 
> Adding the ability to rank three of the candidates of the surrounding 
> small group would offer a pretty good vocabulary of typical 
> green/right/feminist opinions. And since the three would be from a 
> relatively small set (maybe 5 out of 100) the number of combinations 
> might still be safe (reduce the allowed number of ranked candidates to 
> two or one if needed).

Assume that a voter votes for the green wing of the social democrat 
party. Would you then have LocalGreen > LocalOtherSocialDemocrat > 
FarawayGreen, or LocalGreen > FarawayGreen > LocalOtherSocialDemocrat ?

I guess the statement that political proportionality is more important 
than geographical proportionality would force the second ballot.

Also, how would you get parties to cooperate in making a tree? The party 
may say that party unity is too important and therefore pass an internal 
rule that no member may create a subgroup. This is kind of like the 
problem when a party is in majority and that power is contingent upon 
closed list PR; then the party won't want to change to open list PR. 
However, in that case, opinion shifts could cause the party to lose its 
grip on power, but the party always has power over its own organization.