# [EM] Manipulation Resistant Voting

Susan Simmons suzerainsimmons at outlook.com
Sat Jul 17 20:48:08 PDT 2021

```So far we have an election method that is non-manipulable to the extent that we can construct a clone-independent decision tree by a non-manipulable process, which in turn can be easily done with standard software if we can construct a suitable metric on the candidates via a manipulation free process.

That's where Marissa, an ex-NSA data analyst, fits into Bull's trial science corporation ... she's the one who knows how to find mirror juries.

Amazon, FaceBook, and Google have their counterparts to Marissa in real life, and they share/sell their data with/to the NSA ... in other words, there is no need to invent a psycho/political metric on the candidates ... there already exists such a metric on the psycho/political/consumer space of all Americans (and far more).

Bull the TV series is based partly on work pioneered by Doctor Phil before he became a TV personality. In the series his staff resorts to hacking internet data banks only as a last resort. Absent these hackers we might have to construct our own less elaborate metric on our candidates. But it is good to keep in mind that, at least in principle, the problem is already solved.

Her's one way to construct a binary tree given a suitable metric d(p, q) expessing the distance between p and q in candidate space:

Find two candidates p and q such that the furthest distance that any other candidate X would have to go to reach the closer of them is as small as possible. In other words find the smallest radius r such that neighborhoods of radius r centered at p and q contain (in their union) all of the candidates.

The root node of the tree, branches to the points closest to p and those closest to q.

Now recursively organize these two (Voronoi/Dirichlet) sets into subtrees.

That's it!

Sent from my MetroPCS 4G LTE Android Device
-------- Original message --------
From: Susan Simmons <suzerainsimmons at outlook.com>
Date: 7/17/21 2:12 PM (GMT-08:00)
To: Kristofer Munsterhjelm <km_elmet at t-online.de>, election-methods at lists.electorama.com
Subject: Re: [EM] Manipulation Resistant Voting

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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