# [EM] Manipulation Resistant Voting

Susan Simmons suzerainsimmons at outlook.com
Sat Jul 17 14:12:54 PDT 2021

I'm sure that Gibbard considers clone dependence a vulnerability to manipulation. In this case, that vulnerability is limited to the possibility of lying on the questionaires eliciting the information for the construction of the decision tree. If the decision tree is generated randomly, then we are leaving determinism behind.

The Gibbard–Satterthwaite theorem states roughly that every deterministic voting rule is manipulable, except possibly in two cases: if there is a distinguished voter who has a dictatorial power, or if the rule limits the possible outcomes to two options only.

Once the decision tree has been constructed all decisions are of this binary type.

It may be true that Gibbard-Satterthwaite applies more or less to any deterministic democratic process that could be used to generate a decision tree.

In that case a proportionally fair stochastic procedure for generating the decision tree might be the best way forward.

At least, in my opinion, we have isolated the potential source of manipulability. What other methods make such a clean divide between voting day decisions and the possibilities of manipulation?

But enough abstract non-sense ... let's consider some practical possibilities for construction of the decision tree.

My best idea is to use standard decision tree software based on a metric (distance relation) on the leaves (candidates) of the tree.

So our problem becomes how to minimize manipulation of the information forming the basis for the metric on the candidates.

Suppose as a first approximation we ask the candidates themselves to estimate the distances between the various candidates on the various issues. They might be tempted to distort the truth to influence the structure of the decision tree to their advantage.

Not to worry ...instead of taking their estimates at face value by averaging them together ... suppose we pay more attention to how similar they are in their responses.

Then it doesn't matter so much if they try to distort the truth to their advantage, the closer they are to each other in candidate space, the more similar their responses, whether sincere or feigned.

So the distance function is not based per se on their distance estimates, but rather on the distance between their patterns of answers.

Their answer patterns are recorded as arrays of numbers called "data vectors." There are many possible "norms" for measuring the "magnitude" of a data vector.

The distance between two candidates is taken to be the magnitude of the difference between their pattern-of-response vectors.

This is the kind of psychometrics used by the NSA and other data miners to map out your precise location in political/consumer space without even listening in on your phone conversations.

The TV series Bull is based on this kind of psychometric analysis of jurors for finding "mirror jurors" that are very close in psychological distance from the actual jurors. Bull is a trial scientist who can predict the reaction of the actual jurors on the basis of the respective mirror juror reactions.

Do you find this to be interesting?

Sent from my MetroPCS 4G LTE Android Device

-------- Original message --------
From: Kristofer Munsterhjelm <km_elmet at t-online.de>
Date: 7/17/21 10:18 AM (GMT-08:00)
To: Susan Simmons <suzerainsimmons at outlook.com>, election-methods at lists.electorama.com
Subject: Re: [EM] Manipulation Resistant Voting

On 17.07.2021 04:58, Susan Simmons wrote:
>
> It is well known that there is no incentive for dishonest voting when
> the method is to elect the candidate indicated on a randomly chosen
> secret ballot.
>
> Is there also a manipulation free deterministic method?

Doesn't Gibbard's theorem answer that in the negative?

-km
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