# [EM] (3) ?goal of a better election method?

Kevin Venzke stepjak at yahoo.fr
Thu Feb 23 17:20:36 PST 2017

```Hi Steve,
Well, it seems clear to me that page 15 and slides 158-163 are talking about the same concept of being "partially strategy-proof-in-ranking." In both places the explanation offered by the authors is purely talking about how many candidates (out of a pair of two) a single voter might be able to adjust (in terms of their final grade). I think Kristofer gave the same interpretation on Jan 4 (although at the time I didn't understand the point).
That is to say, when you describe page 15 as suggesting that a voter is unlikely to be able to change a result, I feel this is not relevant to this page. It's mathematically not possible at all to contrive a scenario where a single voter who rated A>B can change his ballot in a way to adjust the final grades of both A and B when (in the original outcome) B had a higher final grade than A. They're saying it may be possible for a voter to affect the grade of one, but he won't ever be able to affect the grade of both.
On page 15 as you quote, they seem to conclude from this discussion that MJ "cuts in half the probability of manipulation." I find it confusing that they would call this "cut in half" and that they would call this "manipulation" without some additional explanation, but I don't see how page 15 offers any other interpretation of what they're referring to.
Regarding pages 197-198, I suspect these are related to slides 166-171. They both seem to discuss a naive estimate of the possibility that a voter could affect the outcome. That would seem to be a different issue from what's on page 15, yet both are called either "manipulability" or "probability of manipulation." I would note that they say the lowest possible probability is n + 1/2n, but they don't say what is the highest possible probability. We may guess 100%, but would any method actually correspond to that?
I don't really grasp what they are showing with the math: If n is a count of voters, why would probability be expressed in terms of n? Is this really the percentage of voters that can change the result? And if so would that really be just over 50% in the best case? (I wonder if Kristofer has already explained all this and I just didn't read it...)
To clarify one item:>>K: This means that if the relative order of two candidates' final grades is not to the liking of some voter, that voter may be >>able to adjust the grade of one of the candidates, but not both. "One and not two" seems promising as something that has >>been cut by half.
>S:  Does your last phrase indicate that you now accept the validity of B&L’s claim that MJ “cuts” manipulation in “half”?

It indicates that I think "one and not two" is where they are getting "half." If so, I accept that this has been "cut in half," but I'm skeptical that this concept is a good representation of the "manipulability" of an SGF.
Kevin

De : steve bosworth <stevebosworth at hotmail.com>
À : "stepjak at yahoo.fr" <stepjak at yahoo.fr>; "election-methods at lists.electorama.com" <election-methods at lists.electorama.com>
Envoyé le : Jeudi 23 février 2017 8h53
Objet : Re: [EM] (3) ?goal of a better election method?

<!--#yiv8039895279 P {margin-top:0;margin-bottom:0;}-->HI Kevin,
Message: 2
Date: Sun, 19 Feb 2017 19:20:34 +0000 (UTC)
From: Kevin Venzke <stepjak at yahoo.fr>
To: steve bosworth <stevebosworth at hotmail.com>,
"election-methods at lists.electorama.com"
<election-methods at lists.electorama.com>
Subject: Re: [EM] goal of a better election method
Message-ID: <1682602380.1138980.1487532034974 at mail.yahoo.com>
Content-Type: text/plain; charset="utf-8"

S: Also, how exactly does the above relate to Laraki’s slide 170:  "Given an aggregation functionfand inputr= (r1, . . . , rn), letμ−(f,r) =nbre of judges who can decrease the final grade,μ+(f,r) =nbre of judges who can increase the final grade, Letl=probability a judge wishes to increase the final grade. Theprobability of effective-manipulabilityoffis EM(f) =max       max_    l μ+(f,r) + (1−l)μ−(f,r)            r= (r1,...,rn)     0≤l≤1                         n S: I can send you the above formulaes as an attachment if they have been scrambled by your inbox.
K: Leading up to slide 150, [Laraki] argues that *if* your goal is simply for candidate X to get a grade of 7, then under order functions like MJ, your best strategy is to rate that candidate a 7. Under Range this is not true, because if that candidate is sitting at a 1, rating him a 10 would drag him towards a 7 rating faster than just rating him a 7 would. There is no "half" to be found here; it doesn't seem that any SGF could outperform MJ on this measure.
On slide 158 they describe the concept of being "partially strategy-proof-in-ranking." This means that if the relative order of two candidates' final grades is not to the liking of some voter, that voter may be able to adjust the grade of one of the candidates, but not both. "One and not two" seems promising as something that has been cut by half. S: Does your last phrase indicate that you now accept the validity of B&L’s claim that MJ “cuts” manipulation in “half”?
K: Then on 163 they say that order functions are the only SGFs that have this property.
What do you think, is there a better suggestion for something that has been halved? I would sort of hope so because if the answer is always either "one candidate" or "both candidates" that means there are only two outcomes for a test we're taking as a representation of manipulability under SGFs. S: I hope to understand the point you are making here after receiving your help and comments on all the above. I look forward to your feedback.Steve

De?: steve bosworth <stevebosworth at hotmail.com>
??: "stepjak at yahoo.fr" <stepjak at yahoo.fr>; "election-methods at lists.electorama.com" <election-methods at lists.electorama.com>
Envoy? le : Dimanche 19 f?vrier 2017 3h03
Objet?: [EM] goal of a better election method

Message: 2
Date: Sun, 12 Feb 2017 17:31:37 +0000 (UTC)
From: Kevin Venzke <stepjak at yahoo.fr>
To: steve bosworth <stevebosworth at hotmail.com>,? EM list
??????? <election-methods at electorama.com>
Subject: Re: [EM] ?goal of a better election method?
Message-ID: <1346455147.4984684.1486920697303 at mail.yahoo.com>
Content-Type: text/plain; charset="utf-8"

Hi Kevin:
> S: Secondly, I believe that B&L ? prove? (pp. 15, 19, 186-198) that MJ provides only about ? half? the incentives? >or opportunities for anti-democratic ?strategic? voting to be successful. If you disagree, please explain the flaw in their argument.

K: What I understood from Kristofer's Jan 4 explanation of page 15 is that?this halving of the manipulability is not meant to be a comparison to?any other methods. It's a comparison to a (rather strange) hypothetical situation. If so, this claim on its own could be true but is of unclear value.
Possibly this argument is used to build up to a larger argument. But when it gets stated on its own it feels misleading to me, because there's no way for the reader to understand what this "half" is half of. S: No, B&L clearly explain why MJ provides only about ?half? of the incentives and opportunities to ?manipulate? the results as compared to all the methods that gain their results by ?summing? or ?averaging? all the votes.? In his reply to me, Kristofer also gave me a link to the following source in which B&L concisely state the same claim on slide 150.?  This is in the middle of their discussion of ?strategy?, i.e. between slides 143 & 185: Kristofer: See this slide set by B&L for more on that:
http://igm.univ-mlv.fr/AlgoB/algoperm2012/01Laraki.pdf .
| Majority Judgement - Measuring, Ranking and Electing igm.univ-mlv.frTraditional Methods and results Incompatibility Between Electing and Ranking Majority Judgement: Two Applications Majority Judgement Measuring, Ranking and Electing |

I look forward to your feedback.
| Majority Judgement - Measuring, Ranking and Electingigm.univ-mlv.frTraditional Methods and results Incompatibility Between Electing and Ranking Majority Judgement: Two Applications Majority Judgement Measuring, Ranking and Electing |

SteveKevin
++++++++++++++++++++++
2. Re: ?goal of a better election method? (Kevin Venzke)

Message: 2
Date: Sun, 12 Feb 2017 17:31:37 +0000 (UTC)
From: Kevin Venzke <stepjak at yahoo.fr>
To: steve bosworth <stevebosworth at hotmail.com>,  EM list
<election-methods at electorama.com>
Subject: Re: [EM] ?goal of a better election method?
Message-ID: <1346455147.4984684.1486920697303 at mail.yahoo.com>
Content-Type: text/plain; charset="utf-8"

Hi Kevin:
> S: Secondly, I believe that B&L ? prove? (pp. 15, 19, 186-198) that MJ provides only about ? half?  the incentives? >or opportunities for anti-democratic ?strategic? voting to be successful. If you disagree, please explain the flaw in their argument.

K: What I understood from Kristofer's Jan 4 explanation of page 15 is that? this halving of the manipulability is not meant to be a comparison to ?any other methods. It's a comparison to a (rather strange) hypothetical situation. If so, this claim on its own could be true but is of unclear value.
Possibly this argument is used to build up to a larger argument. But when it gets stated on its own it feels misleading to me, because there's no way for the reader to understand what this "half" is half of.

S: No, B&L clearly explain why MJ provides only about ?half? of the incentives and opportunities to ?manipulate? the results as compared to all the methods that gain their results by ?summing? or ?averaging? all the votes.  In his reply to me, Kristofer also gave me a link to the following source in which B&L concisely state the same claim on slide 150.  This is in the middle of their discussion of ?strategy?, i.e. between slides 143 & 185:

Kristofer: See this slide set by B&L for more on that:
http://igm.univ-mlv.fr/AlgoB/algoperm2012/01Laraki.pdf .
| Majority Judgement - Measuring, Ranking and Electingigm.univ-mlv.frTraditional Methods and results Incompatibility Between Electing and Ranking Majority Judgement: Two Applications Majority Judgement Measuring, Ranking and Electing |

| Majority Judgement - Measuring, Ranking and Electingigm.univ-mlv.frTraditional Methods and results Incompatibility Between Electing and Ranking Majority Judgement: Two Applications Majority Judgement Measuring, Ranking and Electing |

Majority Judgement - Measuring, Ranking and Electing<http://igm.univ-mlv.fr/AlgoB/algoperm2012/01Laraki.pdf>
igm.univ-mlv.fr
Traditional Methods and results Incompatibility Between Electing and Ranking Majority Judgement: Two Applications Majority Judgement Measuring, Ranking and Electing

I look forward to your feedback.

Steve

Kevin

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