Re: [EM] Fwd: SODA, negotiation, and weak CWs
2011/12/25 > Jameson asked for "thoughts." > > My first thought is that this kind of analysis is exactly what we need. > > My second thought is that so far SODA has held up well under all the > probes for weakness that anybody has > come up with. SODA seems to be a very robust method. > My third thought is that I have never seen this kind of soul searching or > probing directed at IRV by IRV > enthusiasts. > Thanks, that's very flattering... but not quite how I'd put it. I don't think I was doing a hard-nosed search for SODA's weaknesses in this case. By picking a set of cases which are at the absolute limit of what any method could handle on a good day, I was more scraping the bottom of the barrel for yet another outstanding strength to ascribe to SODA. And here's what I found: - Preferential methods can't be sensitive to utility (duh.) - Honest range can (duh. But remember, Range has some of the strongest strategy incentives of any method, so honest range may be rare.) - Honest MJ and approval can, as long as voters have some randomness/ spread. (And they have significantly less strategy incentive than Range.) - With strategy, these rated systems can fail the given scenarios badly (chicken dilemma) - Honest, rational SODA cannot be sensitive to utility. - However, it at least avoids the chicken dilemma (and thus has effectively no strategy incentive at all.) - SODA may be able to be sensitive to utilities if candidates act meta-rationally (in ways that experiments such as the ultimatum game show that people sometimes do). I'd say that this shows that SODA handles the set of scenarios as well as any method and better than most. But I can't really say that SODA shines as the clearly best method in these cases. Jameson > > > > Date: Sun, 25 Dec 2011 11:28:24 -0600 > > From: Jameson Quinn > > To: EM > > Subject: [EM] Fwd: SODA, negotiation, and weak CWs > > Message-ID: > > > > Content-Type: text/plain; charset="iso-8859-1" > > > > I'm resubmitting this in a text-friendly format, at Forest's > > request. I'll > > also take the opportunity to add one paragraph about how rated > > methods can > > fail to find the highest-utility candidates in scenarios like > > this. Added > > text is marked ADDED. > > > > -- Forwarded message -- > > From: Jameson Quinn > > Date: 2011/12/25 > > Subject: SODA, negotiation, and weak CWs > > To: EM > > > > > > In order to have optimum Bayesian Regret, a voting system should > > be able to > > not elect a Weak Condorcet Winner (WCW), that is, a CW whose > > utility is > > lower than the other candidates. Consider the following payout > > matrices:Group Size Candidate Utilities > > Scenario 1 (zero sum) A B C > > a 4 4 1 0 > > b 2 0 3 2 > > c 3 0 2 4 > > Total utility 16 16 16 > > > > Scenario 2 (pos. sum) A B C > > a 4 3 1 0 > > b 2 0 3 1.5 > > c 3 0 2 3 > > Total utility 12 16 12 > > > > Scenario 3 (neg. sum) A B C > > a 4 4 0.5 0 > > b 2 0 3 2 > > c 3 0 1 4 > > Total utility 16 11 16 > > > > > > All three scenarios consist of 3 groups of voters: groups a, b, > > and c, with > > 4, 2, and 3 voters respectively, for a total of 9 voters. All > > scenarioshave 3 candidates: A, B, and C, who favor their > > respective groups. And in > > all three scenarios, candidate B is the CW, because the > > preference matrix > > is always > > > > 4: A>B > > 2: B>C > > 3: C>B > > > > But in scenario 1, the utilities of the three candidates are > > balanced; in > > scenario 2, B has the highest utility; and in scenario 3, A and > > C have the > > highest utilities. > > > > Obviously, any purely preferential system will tend to give the > > same result > > in all three scenarios. This might not be 100% true if strategy > > propensitydepended on the utility payoff of a strategy; but the > > strategicpossibilities would have to be just right for a method > > to "get it right" > > for this reason. > > > > It's easy to see how Range could "get it right" in scenarios 2 > > and 3. With > > just a bit of strategy, it's also easy to see how it could > > successfullyfind the CW in scenario 1. > > > > You can also construct plausible stories of how Approval or MJ > > could "get > > it right" in all 3 scenarios, although it probably involves > > adding some > > random noise to voting patterns rather than assuming pure > > "honest" votes. > > > > ADDED: Of course, Range, Approval, and MJ can all get these scenarios > > "wrong" too. Because the scenarios present a classic chicken dilemma > > between B and C, these rated systems could all end up electing A, > > regardless of utility. > > > > But what about SODA? As a primarily preferential system, it > > seems that it > > should give the same result in all three scenarios. If > > candidates all > > rationally pursue the interests of their primary constituency, > > then A will > > approve B to prevent B from having to approve C, leaving a win > > for B. > > > > But if candidate A decides to make an
[EM] Who wronged the A-plumpers
Mike, A voting method algorithm stands or falls by its properties, i.e. its criterion compliances and failures. Another school of thought is less concerned about strict pass/fails of criteria and stresses how well the method does in computer simulations at maximising "social utility" and/or minimising negative emotions like "regret". Before continuing, though, I should clarify that "middle" isn't the best descriptive name for what a middle rating means or is used for. Instead of calling it a middle rating, let's call it (on the ballot) an "accept coalition" rating. Let's call the ratings on the ballot "top" and "accept coalition". If you don't give a rating to a candidate, we can call that a "bottom rating". A voter "accepts" a candidate if s/he votes hir top or merely gives to hir an "accept coalition" rating. Ballots are simply for voters to register their (hopefully and "officially" presumably sincere) preferences among the candidates, not to formally issue open invitations to the voters to play sordid strategy games. For the method to wrong someone, it has to act wrongly or wrongfully. That is nicely circular...granted. But let's consider what MMT does, to judge whether what it does is wrong: You then go on to more-or-less explain the details of MMT's algorithm, putting a big positive spin on each of its components. Now, please note that I'm not using MMT's rule to justify MMT's rule. I'd like to "note" that, but I can't see what else you are doing. Among the candidates in those mutual majority sets, MMT elects the most popular one (the one with the most top-ratings). Defining "popular" that way instead of say "fewest bottom-ratings" or "best top-ratings minus bottom-ratings score" (or perhaps even by some non-positional measure) looks quite arbitrary and uncompelling How wrong is it to elect the most popular candidate among those among whom majority has determined that the winner must be chosen? It's "wrong" because it's an algorithm that needlessly fails some desirable criteria. There are other methods (and there need only be one) that don't fail those criteria while sharing all of MMT's desirable criterion compliances. MMT's rules were chosen to achieve FBC compliance, avoid the co-operation/defection problem, and enforce majority rule in some way. That is fine and admirable, but there are much better methods that do the same thing. Sincere preferences: 49: C 27: A>B 24: B>A 20: A The A>B and B>A voters should obviously coalition-accept each other's candidates. What should the 20 A voters do, who are indifferent between B and C? Well, they should know that A probably doesn't have top ratings from a majority of the voters. And they should know that A probably is not even the Plurality winner. Err... why should they "know" that? A's top-ratings score is 47, not far behind C's top-ratings score of 49. If all the voters have very good information about each others' preferences and are aware of and happy to use the best strategy (no matter how insincere or weird) then all deterministic methods are about as good as each other at picking the right winner. And how does Chris justify saying that the result is "wrong"? He says that it shouldn't be possible for voters to foul up their voted-favorite's chance of winning. No, that would refer to Mono-add-Top. I said that methods must meet Mono-add-Plump (compared to which Mono-add-Top is a bit arbitrary and "expensive"). Also the result gives bad failures of other criteria, like the tied-at-the-top rule modified pairwise beats-all criterion (compatible with FBC etc.) and my new "Add-Top Proofed Solid-Coalition Majority" criterion (doubtless also compatible with FBC, ABE etc.) and Condorcet Loser. Could there be a method that would protect the A-plumpers from their own stupidity? Sure. Is the voting system obligated to do that? No. The voters are adults, responsible for their own actions. If the "stupidity" is just honest voting, then the voting system is obligated to protect those voters if it can (without giving up some other desirable property). If the honest voting is just plumping, I say that the voting system can do that easily. And notice that though Chris is affronted by noncompliance with Mono-Add-Plump, by an FBC/ABE method, Chris isn't bothered by IRV's particularly flagrant form of nonmonotonicity. Why the inconsistency and self-contradiction, Chris? You might have got a clue from what I wrote in an earlier post: "...if failure of Mono-add-Plump isn't self-evidently *completely ridiculous* (and so much so that anything not compatible with Mono-add-Plump compliance is thereby made a complete nonsense of), then I have no idea what is. The only way this view of mine could be dented (and I made a bit wiser and sadder) is if it was proved to me that compliance with Mono-add-Plump isn't compatible with some other cl
[EM] Proportional Range Voting via Honest Approval PAV
While writing the below it occurred to me that we could construct another Proportional Representation method based on ordinal ballots (ranked preferences) by the following technique: (1) Convert the ordinal rankings into cardinal ratings via the monotonic, clone free techinque that I outlined under the title "Borda Done Right" a few months back. (2) Convert these ratings into approval style ballots via the honest approval strategy. (3) Apply PAV to the resulting ballot set. Here's a brief review of the ballot conversion at the heart of Borda Done Right: For each candidate C on the ballot in question let p(C) be the probability that a candidate ranked equal to or behind C would be elected in a random favorite election. Then treating these probabilities as scores, normalize them to a cardinal ratings scale of zero to one. [Any other monotone, clone free lottery could be used in place of the random favorite lottery in the definition of p(C).] I would be interested to see some simulations comparing this ordinal-->cardinal-->approval--->PAV method of PR with other PR methods based on rankings. Since all of the steps are monotone and clone proof, the composite method should share these properties to the extent that PAV does. My Best to You All on this holiday weekend! Forest > - > Date: Sun, 25 Dec 2011 16:40:50 + (GMT) > From: fsimm...@pcc.edu > To: election-methods@lists.electorama.com > Subject: [EM] Proportional Range Voting via Honest Approval PAV >> Now that we have a good definition of honest approval strategy, > we can automatically adapt methods > (like PAV) that are based on approval style ballots to cardinal > ratings style ballots. > > Definition: Honest Approval Strategy: Approve your k top ranked > candidates, where k is the sum of > your cardinal ratings (on a scale of zero to one) rounded to the > nearest whole number. > > So given a set of Range/Score/Grade ballots, first convert them > to cardinal ratings on a scale of zero to > one. Then use honest approval strategy to convert these ratings > ballots to approval style ballots. > Finally apply PAV (or whatever approval method you like) to > determine who gets elected. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Fwd: SODA, negotiation, and weak CWs
Jameson asked for "thoughts." My first thought is that this kind of analysis is exactly what we need. My second thought is that so far SODA has held up well under all the probes for weakness that anybody has come up with. SODA seems to be a very robust method. My third thought is that I have never seen this kind of soul searching or probing directed at IRV by IRV enthusiasts. > Date: Sun, 25 Dec 2011 11:28:24 -0600 > From: Jameson Quinn > To: EM > Subject: [EM] Fwd: SODA, negotiation, and weak CWs > Message-ID: > > Content-Type: text/plain; charset="iso-8859-1" > > I'm resubmitting this in a text-friendly format, at Forest's > request. I'll > also take the opportunity to add one paragraph about how rated > methods can > fail to find the highest-utility candidates in scenarios like > this. Added > text is marked ADDED. > > -- Forwarded message -- > From: Jameson Quinn > Date: 2011/12/25 > Subject: SODA, negotiation, and weak CWs > To: EM > > > In order to have optimum Bayesian Regret, a voting system should > be able to > not elect a Weak Condorcet Winner (WCW), that is, a CW whose > utility is > lower than the other candidates. Consider the following payout > matrices:Group Size Candidate Utilities > Scenario 1 (zero sum) A B C > a 4 4 1 0 > b 2 0 3 2 > c 3 0 2 4 > Total utility 16 16 16 > > Scenario 2 (pos. sum) A B C > a 4 3 1 0 > b 2 0 3 1.5 > c 3 0 2 3 > Total utility 12 16 12 > > Scenario 3 (neg. sum) A B C > a 4 4 0.5 0 > b 2 0 3 2 > c 3 0 1 4 > Total utility 16 11 16 > > > All three scenarios consist of 3 groups of voters: groups a, b, > and c, with > 4, 2, and 3 voters respectively, for a total of 9 voters. All > scenarioshave 3 candidates: A, B, and C, who favor their > respective groups. And in > all three scenarios, candidate B is the CW, because the > preference matrix > is always > > 4: A>B > 2: B>C > 3: C>B > > But in scenario 1, the utilities of the three candidates are > balanced; in > scenario 2, B has the highest utility; and in scenario 3, A and > C have the > highest utilities. > > Obviously, any purely preferential system will tend to give the > same result > in all three scenarios. This might not be 100% true if strategy > propensitydepended on the utility payoff of a strategy; but the > strategicpossibilities would have to be just right for a method > to "get it right" > for this reason. > > It's easy to see how Range could "get it right" in scenarios 2 > and 3. With > just a bit of strategy, it's also easy to see how it could > successfullyfind the CW in scenario 1. > > You can also construct plausible stories of how Approval or MJ > could "get > it right" in all 3 scenarios, although it probably involves > adding some > random noise to voting patterns rather than assuming pure > "honest" votes. > > ADDED: Of course, Range, Approval, and MJ can all get these scenarios > "wrong" too. Because the scenarios present a classic chicken dilemma > between B and C, these rated systems could all end up electing A, > regardless of utility. > > But what about SODA? As a primarily preferential system, it > seems that it > should give the same result in all three scenarios. If > candidates all > rationally pursue the interests of their primary constituency, > then A will > approve B to prevent B from having to approve C, leaving a win > for B. > > But if candidate A decides to make an ultimatum, things could go > differently. A says to B: "Make some promise that transfers 0.5 > point of > utility to each member of group a, or I will not approve you." > Assume that > B can make a promise to transfer utility from one group to > another at 80% > efficiency; and that such promises are not strictly enforceable. > Thus, if A > gets too greedy, B can simply promise the moon and not keep the > promise;but if A asks for something reasonable, B will see > honesty as worth it. > > B could promise to transfer 0.5 point of utility from groups b > and c to > group a. Since utility transfers are assumed to be only 80% > efficient, that > transfer of 2.5 utility points would result in a net loss of > 0.5. So the > payoffs would be: > > Group Size Candidate Utilities > Scenario 1a(zero sum) A B C > a 4 4 1.5 0 > b 2 0 2.5 2 > c 3 0 1.5 4 > Total utility 16 15.5 16 > > Group Size Candidate Utilities > Scenario 1b(zero sum) A B C > a 4 4 1.5 0 > b 2 0 3 2 > c 3 0 1.1 4 > Total utility 16 15.3 16 > > Scenario 2a(pos. sum) A B C > a 4 3 1.5 0 > b 2 0 2.5 1.5 > c 3 0 1.5 3 > Total utility 12 15.5 12 > > Scenario 3a(neg. sum) A B C > a 4 4 1 0 > b 2 0 2.5 2 > c 3 0 0.5 4 > Total utility 16 10.5 16 > > Scenario 3b(neg. sum) A B C > a 4 4 1 0 > b 2 0 3 2 > c 3 0 0.1 4 > Total utility 16 10.3 16 > > Note that in scenarios 1a and 2a, this utility transfer has left > B giving > the same utility to groups a and c, while in scenario 3a, B has > switchedfrom favoring group c over group a, to favoring group a > over group c. Also, > note
[EM] Fwd: SODA, negotiation, and weak CWs
I'm resubmitting this in a text-friendly format, at Forest's request. I'll also take the opportunity to add one paragraph about how rated methods can fail to find the highest-utility candidates in scenarios like this. Added text is marked ADDED. -- Forwarded message -- From: Jameson Quinn Date: 2011/12/25 Subject: SODA, negotiation, and weak CWs To: EM In order to have optimum Bayesian Regret, a voting system should be able to not elect a Weak Condorcet Winner (WCW), that is, a CW whose utility is lower than the other candidates. Consider the following payout matrices: Group SizeCandidate Utilities Scenario 1 (zero sum) A B C a 4 4 1 0 b 2 0 3 2 c 3 0 2 4 Total utility 16 16 16 Scenario 2 (pos. sum) A B C a 4 3 1 0 b 2 0 3 1.5 c 3 0 2 3 Total utility 12 16 12 Scenario 3 (neg. sum) A B C a 4 4 0.5 0 b 2 0 3 2 c 3 0 1 4 Total utility 16 11 16 All three scenarios consist of 3 groups of voters: groups a, b, and c, with 4, 2, and 3 voters respectively, for a total of 9 voters. All scenarios have 3 candidates: A, B, and C, who favor their respective groups. And in all three scenarios, candidate B is the CW, because the preference matrix is always 4: A>B 2: B>C 3: C>B But in scenario 1, the utilities of the three candidates are balanced; in scenario 2, B has the highest utility; and in scenario 3, A and C have the highest utilities. Obviously, any purely preferential system will tend to give the same result in all three scenarios. This might not be 100% true if strategy propensity depended on the utility payoff of a strategy; but the strategic possibilities would have to be just right for a method to "get it right" for this reason. It's easy to see how Range could "get it right" in scenarios 2 and 3. With just a bit of strategy, it's also easy to see how it could successfully find the CW in scenario 1. You can also construct plausible stories of how Approval or MJ could "get it right" in all 3 scenarios, although it probably involves adding some random noise to voting patterns rather than assuming pure "honest" votes. ADDED: Of course, Range, Approval, and MJ can all get these scenarios "wrong" too. Because the scenarios present a classic chicken dilemma between B and C, these rated systems could all end up electing A, regardless of utility. But what about SODA? As a primarily preferential system, it seems that it should give the same result in all three scenarios. If candidates all rationally pursue the interests of their primary constituency, then A will approve B to prevent B from having to approve C, leaving a win for B. But if candidate A decides to make an ultimatum, things could go differently. A says to B: "Make some promise that transfers 0.5 point of utility to each member of group a, or I will not approve you." Assume that B can make a promise to transfer utility from one group to another at 80% efficiency; and that such promises are not strictly enforceable. Thus, if A gets too greedy, B can simply promise the moon and not keep the promise; but if A asks for something reasonable, B will see honesty as worth it. B could promise to transfer 0.5 point of utility from groups b and c to group a. Since utility transfers are assumed to be only 80% efficient, that transfer of 2.5 utility points would result in a net loss of 0.5. So the payoffs would be: Group SizeCandidate Utilities Scenario 1a(zero sum) A B C a 4 4 1.5 0 b 2 0 2.5 2 c 3 0 1.5 4 Total utility 16 15.516 Group SizeCandidate Utilities Scenario 1b(zero sum) A B C a 4 4 1.5 0 b 2 0 3 2 c 3 0 1.1 4 Total utility 16 15.316 Scenario 2a(pos. sum) A B C a 4 3 1.5 0 b 2 0 2.5 1.5 c 3 0 1.5 3 Total utility 12 15.512 Scenario 3a(neg. sum) A B C a 4 4 1 0 b 2 0 2.5 2 c 3 0 0.5 4 Total utility 16 10.516 Scenario 3b(neg. sum) A B C a 4 4 1 0 b 2 0 3 2 c 3 0 0.1 4 Total utility 16 10.316 Note that in scenarios 1a and 2a, this utility transfer has left B giving the same utility to groups
[EM] Approval Strategy
Mike wrote > > As for myself, in Score-Voting, I'd probably use non-extreme > > points assignments only in two instances: > > > > 1. The excellent diplomatic ABE solution that you suggested > for > > Score-Voting > Forest replied > Excellent except that satisfaction of the FBC is in doubt. I assumed you meant my Smith//Range proposal (for which FBC is in doubt). But you probably meant my more recent MMMPO aka LRV which does satisfy the FBC. In the first method zero info strategy does take care of the ABE defection problem, but potential failure of the FBC is bad for a public proposal. Election-Methods mailing list - see http://electorama.com/em for list info
[EM] SODA, negotiation, and weak CWs (Jameson Quinn)
Jameson, could you please submit this again in a plain text format that doesn't put in extra form feeds? Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Proportional Range Voting via Honest Approval PAV
Now that we have a good definition of honest approval strategy, we can automatically adapt methods (like PAV) that are based on approval style ballots to cardinal ratings style ballots. Definition: Honest Approval Strategy: Approve your k top ranked candidates, where k is the sum of your cardinal ratings (on a scale of zero to one) rounded to the nearest whole number. So given a set of Range/Score/Grade ballots, first convert them to cardinal ratings on a scale of zero to one. Then use honest approval strategy to convert these ratings ballots to approval style ballots. Finally apply PAV (or whatever approval method you like) to determine who gets elected. Election-Methods mailing list - see http://electorama.com/em for list info
