Re: [EM] Amalgamation details, hijacking, and free-riding
Well, kinda; but in a sense, that pushes the strategy into the tree-building. 2011/8/6 Juho Laatu juho4...@yahoo.co.uk On 4.8.2011, at 2.09, Jameson Quinn wrote: Free riding in some form is inevitable in a good system. (That is, any system which avoids free riding entirely would be horribly warped by that necessity). How about tree methods? If candidates are ordered as a binary tree (instead of an open list), then there are no choices between three or more branches, and related free riding becomes impossible. Juho Election-Methods mailing list - see http://electorama.com/em for list info Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Amalgamation details, hijacking, and free-riding
Tree building could be voluntary or mandatory. If voluntary, then parties and wings can stop free riding in their own area. If mandatory, then the most difficult part is to organize the parties as a tree (= party external tree). One should have rules on how to build a tree also in the case when there is no consensus on what the structure of the tree should be. One simple approach would be to allow the already agreed (= voluntary) binary branches (= trees of a forest) to join themselves (or the bigger trees that they are already part of) into other trees of the forest in random order. Or maybe largest ones first into the largest tree, starting from the third largest, after joining the two largest ones together first. I assumed that the voluntary branches (that were agreed already before the forced phase) would be considered atomic (= no joining inside them). Did you mean that there would be concrete strategic opportunities in the tree-bulding phase, or that one just needs to think a bit on how to form the tree or how to force the tree to be formed? Sincere strategy seems quite good to me. Or maybe one could nominate fake parties next to one's strongest competitors in the hope of making some of the voters of the competing party vote for the wrong party (that could get a seat if many enough voters make that mistake). Juho P.S. I might come back with a proposal of considering trees to be a good method that is simple and understandable to the voters, very strategy free, and even close to but better than plurality. On 6.8.2011, at 10.46, Jameson Quinn wrote: Well, kinda; but in a sense, that pushes the strategy into the tree-building. 2011/8/6 Juho Laatu juho4...@yahoo.co.uk On 4.8.2011, at 2.09, Jameson Quinn wrote: Free riding in some form is inevitable in a good system. (That is, any system which avoids free riding entirely would be horribly warped by that necessity). How about tree methods? If candidates are ordered as a binary tree (instead of an open list), then there are no choices between three or more branches, and related free riding becomes impossible. Juho Election-Methods mailing list - see http://electorama.com/em for list info Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Record activity on the EM list?
Juho Laatu Sent: Thursday, August 04, 2011 5:12 PM On 4.8.2011, at 14.21, James Gilmour wrote: There is only one real issue in elections: representation of the voters. If in a single winner partisan election the voters vote 51% for A and 49% for B, we have a major problem in representation. Ok, 49% of the voters without representation. This throws the problem into its sharpest perspective. There are related, difficult problems when there are three, four or more candidates for the one seat. If one uses single-member districts to elect multiple representatives, then this means also some randomness in the results. This is not really a problem of single-winner methods themselves but a problem in how they are used (as multi-winner methods). I agree. It is fundamentally wrong to use any single-winner, single-member district voting system to elect the members of a representative assembly (e.g. city council, state legislature). But if the voters vote in the same way (51% to 49%) in a two-member election, any sensible voting system will give one seat to A and one seat to B. Compared to that difference in providing representation of the voters, all the other differences between single-winner and multi-winner elections are trivial. From this point of view single-winner methods are more problematic than multi-winner methods (at least when used to elect multiple representatives from single-member districts). No - not just when (improperly) used to elect the members of a representative assembly. THE problem is inherent in the single-winner election. As you go on to say in your next comment. This problem of single-winner methods is quite impossible to fix (most single-winner methods respect the will of the majority). The extreme problem (51% to 49%) is impossible to fix and so it is the greatest challenge in electoral science to obtain the most representative outcome. In the two-candidate election, the best we can do is to guarantee representation to the majority. The 51% vs. 49% problem is present also in accurately proportional representative bodies since also those bodies may make majority decisions. One way to alleviate this kind of narrow majority related problems is to seek compromise decisions. I have to part company with you here. It should NOT, in my view, be part of the function of the voting system to manipulate the votes to obtain any outcome other than representation of the voters. It is not part of the function of a voting system to seek consensus. If the voters want to vote for candidates who will seek consensus, that's fine - but that is very different for making seek consensus an objective of the voting system. The function of the voting system should simply be to return the most representative result in terms of representing the voters, as expressed by the voters' responses to the candidates who have offered themselves for election. Seeking consensus and not seeking consensus are aspects of how the elected members will behave within the elected assembly. And of course, the voters may rightly take such views into account in their assessments of the candidates before they cast their votes. But that is just part of candidate appraisal. Given a sensitive voting system, the outcome (seats won) will reflect the views of the voters, which may include views on seeking consensus. James That is what in principle happens e.g. in coalition governments. Coalition governments may represent well over 50% of the voters. Let's assume that this is the case. The program of the government may contain multiple topics that would be 51% vs. 49% questions in the representative body or among the voters, but probably all coalition members will get more than they lose. Let's assume that the coalition is heterogeneous so that it does not agree on all the 51% vs. 49% decisions that is has to make. Maybe there are two 51% vs. 49% topics that go the right way against every one such topic that goes wrong. In that way we don't have a narrow majority that always makes 51% decisions but a supermajority that has considerably higher support behind everything it does (although all parties of the coalition do not like all the decisions). In two-party systems the balance is based more on two alternating policies. Often both parties have quite centrist policies since both try to meet the needs of the median voters. In some topics they may however have also clearly opposite positions. I guess the overall policy and results of two-party system governments are typically more 51% majority driven than in multi-party governments. (Coalition governments may however also have only narrow majority and the coalitions may be quite fixed, e.g. left vs. right, and as a result their decisions may follow the 51% majority style.) My point is just that in addition to multi-winner methods
Re: [EM] Record activity on the EM list?
I was also looking for pure proportional representation. The compromise decisions would take place after the election in a representative body or in a government. The election methods need not be tampered. My theory was just that in the case that the majority (of parties) that forms the government is considerably larger than 51% the decisions could have wider support than in the typical 51+% governments of a two-party system. The larger government would have to make compromises that are at least acceptable to all parties in the government. Juho On 6.8.2011, at 17.39, James Gilmour wrote: Juho Laatu Sent: Thursday, August 04, 2011 5:12 PM On 4.8.2011, at 14.21, James Gilmour wrote: There is only one real issue in elections: representation of the voters. If in a single winner partisan election the voters vote 51% for A and 49% for B, we have a major problem in representation. Ok, 49% of the voters without representation. This throws the problem into its sharpest perspective. There are related, difficult problems when there are three, four or more candidates for the one seat. If one uses single-member districts to elect multiple representatives, then this means also some randomness in the results. This is not really a problem of single-winner methods themselves but a problem in how they are used (as multi-winner methods). I agree. It is fundamentally wrong to use any single-winner, single-member district voting system to elect the members of a representative assembly (e.g. city council, state legislature). But if the voters vote in the same way (51% to 49%) in a two-member election, any sensible voting system will give one seat to A and one seat to B. Compared to that difference in providing representation of the voters, all the other differences between single-winner and multi-winner elections are trivial. From this point of view single-winner methods are more problematic than multi-winner methods (at least when used to elect multiple representatives from single-member districts). No - not just when (improperly) used to elect the members of a representative assembly. THE problem is inherent in the single-winner election. As you go on to say in your next comment. This problem of single-winner methods is quite impossible to fix (most single-winner methods respect the will of the majority). The extreme problem (51% to 49%) is impossible to fix and so it is the greatest challenge in electoral science to obtain the most representative outcome. In the two-candidate election, the best we can do is to guarantee representation to the majority. The 51% vs. 49% problem is present also in accurately proportional representative bodies since also those bodies may make majority decisions. One way to alleviate this kind of narrow majority related problems is to seek compromise decisions. I have to part company with you here. It should NOT, in my view, be part of the function of the voting system to manipulate the votes to obtain any outcome other than representation of the voters. It is not part of the function of a voting system to seek consensus. If the voters want to vote for candidates who will seek consensus, that's fine - but that is very different for making seek consensus an objective of the voting system. The function of the voting system should simply be to return the most representative result in terms of representing the voters, as expressed by the voters' responses to the candidates who have offered themselves for election. Seeking consensus and not seeking consensus are aspects of how the elected members will behave within the elected assembly. And of course, the voters may rightly take such views into account in their assessments of the candidates before they cast their votes. But that is just part of candidate appraisal. Given a sensitive voting system, the outcome (seats won) will reflect the views of the voters, which may include views on seeking consensus. James That is what in principle happens e.g. in coalition governments. Coalition governments may represent well over 50% of the voters. Let's assume that this is the case. The program of the government may contain multiple topics that would be 51% vs. 49% questions in the representative body or among the voters, but probably all coalition members will get more than they lose. Let's assume that the coalition is heterogeneous so that it does not agree on all the 51% vs. 49% decisions that is has to make. Maybe there are two 51% vs. 49% topics that go the right way against every one such topic that goes wrong. In that way we don't have a narrow majority that always makes 51% decisions but a supermajority that has considerably higher support behind everything it does (although all parties of the coalition do not like all the decisions). In two-party systems the
[EM] Chicken problem (was: SODA and the Condorcet criterion)
More thoughts on the chicken problem. Again, in Forest's version, that's a scenario like: 48 A 27 CB 25 BC C is the pairwise champion, but B is motivated to truncate, and C to retaliate defensively, until A ends up winning. In my opinion, scenarios like this make the single most intractable practical strategy problem in voting theory: - Approval, Range, and median-based systems all suffer directly. - Most winning-vote-like Condorcet systems fall prey, including otherwise-great systems like Schulze. - Margins systems have no truncation incentive - but as a direct consequence, they give extremely difficult-to-justify results if the B block truncates; in fact, they allow a strategic C block to fool the system into thinking it's seeing this scenarion when actually B and C are mortal enemies. - IRV does relatively well with this scenario - but in return, pays no attention at all to the second choice of the A voters, which should be decisive if it exists. - At the other extreme, some systems resolve this problem by forcing strict rankings from the A voters - but if they really don't have a preference, that ends up being just statistical noise, and doesn't even necessarily remove the game-of-chicken incentives if things are balanced right. Moreover, forcing B and C voters into strict rankings only makes them escalate their truncations into burials. Most of us, when we want to test our voting systems with a difficult case, use a strict-ranking Condorcet cycle of three; the old, standard ABC BCA CAB scenario. That's nice and simple, but not very realistic. To me, the game of chicken scenario; the resulting Condorcet cycle if B truncates; and related scenarios that could strategically be made to masquerade as these; are better practical tests for a voting system. In fact, I'd go so far as to guess that *a real-life Condorcet cycle would be more likely to be the result of playing chicken than of honest preferences.* As Forest already explained, SODA, as currently formulated, resolves the game of chicken — if all votes are delegated. It can do that because games among finite candidates are much more tractable than those among oceans of voters. SODA's sequential trick would be ridiculous with voters; imagine Your turn to vote is on Sunday at 2:35:58 PM. In my previous message in this thread (Re: SODA and the Condorcet criterion), I pointed out that there's still a problem if voters explicitly truncate by refusing to delegate. But I've been considering this issue, and eventually I found a solution that I think is simple enough to include in SODA: *Make all candidate's predeclared rankings into strict rankings by breaking declared ties in order of the current approval totals when it's their turn to use their delegated votes.* So if B voters truncated, candidate A would see that B was headed for a win, and would have the option to delegate to C. All the truncation would have accomplished would be to make A into a kingmaker between B and C. Since A could have had this kingmaker power, if she had wanted it, from the start, that's not a problem. The only difference between this end-game kingmaker power of A's, and if she had simply declared a preference from the start, is that the end-game power could in theory arise no matter which of B or C has more approvals, whereas an initial preference would only confer kingmaker power if the preferred candidate ended up with fewer approvals. Is this version of SODA really the only system to have a fully-satisfactory resolution to the chicken problem? Even if it is, is it worth adding this additional complexity to SODA? Can anyone make a chicken-like scenario which still stumps this SODA version? (If your scenario has more than 4 candidates, please use DAC instead of approval to find the SODA order of play.) Or do you know of a different system which creatively resolves the chicken problem? JQ 2011/8/5 Jameson Quinn jameson.qu...@gmail.com 2011/8/5 fsimm...@pcc.edu Jameson, as you say, it seems that SODA will always elect a candidate that beats every other candidate majority pairwise. If rankings are complete, then all pairwise wins will be by majority. So at least to the degree that rankings are complete, SODA satisfies the Condorcet Criterion. Also, as I mentioned briefly in my last message under this subject heading, SODA seems to completely demolish the chicken problem. Well almost. See below. To review for other readers, we're talking about the scenario 48 A 27 CB 25 BC Candidates B and C form a clone set that pairwise beats A, and in fact C is the Condorcet Winner, but under many Condorcet methods, as well as for Range and Approval, there is a large temptation for the 25 B faction to threaten to truncate C, and thereby steal the election from C. Of course C can counter the threat to truncate B, but then A wins. So it is a classical game of chicken. Some methods like
Re: [EM] Record activity on the EM list?
You can also have minority government (usually single-party), where the majorities are by consensus, issue by issue, transcending the parties. Incidentally, what is pure proportional representation? It is a term I have come across quite frequently. James -Original Message- From: election-methods-boun...@lists.electorama.com [mailto:election-methods-boun...@lists.electorama.com] On Behalf Of Juho Laatu Sent: Saturday, August 06, 2011 5:38 PM To: EM list Subject: Re: [EM] Record activity on the EM list? I was also looking for pure proportional representation. The compromise decisions would take place after the election in a representative body or in a government. The election methods need not be tampered. My theory was just that in the case that the majority (of parties) that forms the government is considerably larger than 51% the decisions could have wider support than in the typical 51+% governments of a two-party system. The larger government would have to make compromises that are at least acceptable to all parties in the government. Juho On 6.8.2011, at 17.39, James Gilmour wrote: Juho Laatu Sent: Thursday, August 04, 2011 5:12 PM On 4.8.2011, at 14.21, James Gilmour wrote: There is only one real issue in elections: representation of the voters. If in a single winner partisan election the voters vote 51% for A and 49% for B, we have a major problem in representation. Ok, 49% of the voters without representation. This throws the problem into its sharpest perspective. There are related, difficult problems when there are three, four or more candidates for the one seat. If one uses single-member districts to elect multiple representatives, then this means also some randomness in the results. This is not really a problem of single-winner methods themselves but a problem in how they are used (as multi-winner methods). I agree. It is fundamentally wrong to use any single-winner, single-member district voting system to elect the members of a representative assembly (e.g. city council, state legislature). But if the voters vote in the same way (51% to 49%) in a two-member election, any sensible voting system will give one seat to A and one seat to B. Compared to that difference in providing representation of the voters, all the other differences between single-winner and multi-winner elections are trivial. From this point of view single-winner methods are more problematic than multi-winner methods (at least when used to elect multiple representatives from single-member districts). No - not just when (improperly) used to elect the members of a representative assembly. THE problem is inherent in the single-winner election. As you go on to say in your next comment. This problem of single-winner methods is quite impossible to fix (most single-winner methods respect the will of the majority). The extreme problem (51% to 49%) is impossible to fix and so it is the greatest challenge in electoral science to obtain the most representative outcome. In the two-candidate election, the best we can do is to guarantee representation to the majority. The 51% vs. 49% problem is present also in accurately proportional representative bodies since also those bodies may make majority decisions. One way to alleviate this kind of narrow majority related problems is to seek compromise decisions. I have to part company with you here. It should NOT, in my view, be part of the function of the voting system to manipulate the votes to obtain any outcome other than representation of the voters. It is not part of the function of a voting system to seek consensus. If the voters want to vote for candidates who will seek consensus, that's fine - but that is very different for making seek consensus an objective of the voting system. The function of the voting system should simply be to return the most representative result in terms of representing the voters, as expressed by the voters' responses to the candidates who have offered themselves for election. Seeking consensus and not seeking consensus are aspects of how the elected members will behave within the elected assembly. And of course, the voters may rightly take such views into account in their assessments of the candidates before they cast their votes. But that is just part of candidate appraisal. Given a sensitive voting system, the outcome (seats won) will reflect the views of the voters, which may include views on seeking consensus. James That is what in principle happens e.g. in coalition governments. Coalition governments may represent well over 50% of the voters. Let's assume that this is the case. The program of the government may contain multiple
Re: [EM] Record activity on the EM list?
Term pure proportional representation was just an ad hoc invention that I used to refer to methods that aim at providing best possible proportional representation and nothing else (no thresholds, no bias, no consensus related stuff). Yes, minority governments need good support in the representative bodies. Since their life depends on having that support, hopefully wider than 51%, they probably make decisions that are intended to please (or at lest be acceptable to) as many parties as possible. Juho On 6.8.2011, at 19.52, James Gilmour wrote: You can also have minority government (usually single-party), where the majorities are by consensus, issue by issue, transcending the parties. Incidentally, what is pure proportional representation? It is a term I have come across quite frequently. James -Original Message- From: election-methods-boun...@lists.electorama.com [mailto:election-methods-boun...@lists.electorama.com] On Behalf Of Juho Laatu Sent: Saturday, August 06, 2011 5:38 PM To: EM list Subject: Re: [EM] Record activity on the EM list? I was also looking for pure proportional representation. The compromise decisions would take place after the election in a representative body or in a government. The election methods need not be tampered. My theory was just that in the case that the majority (of parties) that forms the government is considerably larger than 51% the decisions could have wider support than in the typical 51+% governments of a two-party system. The larger government would have to make compromises that are at least acceptable to all parties in the government. Juho On 6.8.2011, at 17.39, James Gilmour wrote: Juho Laatu Sent: Thursday, August 04, 2011 5:12 PM On 4.8.2011, at 14.21, James Gilmour wrote: There is only one real issue in elections: representation of the voters. If in a single winner partisan election the voters vote 51% for A and 49% for B, we have a major problem in representation. Ok, 49% of the voters without representation. This throws the problem into its sharpest perspective. There are related, difficult problems when there are three, four or more candidates for the one seat. If one uses single-member districts to elect multiple representatives, then this means also some randomness in the results. This is not really a problem of single-winner methods themselves but a problem in how they are used (as multi-winner methods). I agree. It is fundamentally wrong to use any single-winner, single-member district voting system to elect the members of a representative assembly (e.g. city council, state legislature). But if the voters vote in the same way (51% to 49%) in a two-member election, any sensible voting system will give one seat to A and one seat to B. Compared to that difference in providing representation of the voters, all the other differences between single-winner and multi-winner elections are trivial. From this point of view single-winner methods are more problematic than multi-winner methods (at least when used to elect multiple representatives from single-member districts). No - not just when (improperly) used to elect the members of a representative assembly. THE problem is inherent in the single-winner election. As you go on to say in your next comment. This problem of single-winner methods is quite impossible to fix (most single-winner methods respect the will of the majority). The extreme problem (51% to 49%) is impossible to fix and so it is the greatest challenge in electoral science to obtain the most representative outcome. In the two-candidate election, the best we can do is to guarantee representation to the majority. The 51% vs. 49% problem is present also in accurately proportional representative bodies since also those bodies may make majority decisions. One way to alleviate this kind of narrow majority related problems is to seek compromise decisions. I have to part company with you here. It should NOT, in my view, be part of the function of the voting system to manipulate the votes to obtain any outcome other than representation of the voters. It is not part of the function of a voting system to seek consensus. If the voters want to vote for candidates who will seek consensus, that's fine - but that is very different for making seek consensus an objective of the voting system. The function of the voting system should simply be to return the most representative result in terms of representing the voters, as expressed by the voters' responses to the candidates who have offered themselves for election. Seeking consensus and not seeking consensus are aspects of how the elected members will behave within the elected assembly. And of course, the voters may rightly take such views into account in their assessments of
Re: [EM] Chicken problem (was: SODA and the Condorcet criterion)
To review for other readers, we're talking about the scenario 48 A 27 CB 25 BC Candidates B and C form a clone set that pairwise beats A, and in fact C is the Condorcet Winner, but under many Condorcet methods, as well as for Range and Approval, there is a large temptation for the 25 B faction to threaten to truncate C, and thereby steal the election from C. Of course C can counter the threat to truncate B, but then A wins. So it is a classical game of chicken. Some methods like IRV cop out by giving the win to A right off the bat, so there is no game of chicken. Wait a minute! IRV elects C in this scenario, if that is how the voters actually vote, and those are the sincere preferences (A voters have no preference between B and C). Much as I hate to say it, IRV works OK in that scenario. On the other hand, if the A voters prefer B over C, (as in the 2009 Burlington, VT mayoral election, http://scorevoting.net/Burlington.html) IRV ignores the preference and still elects C, which seems to be the wrong choice. Election-Methods mailing list - see http://electorama.com/em for list info
[EM] : Chicken problem (was: SODA and the Condorcet
Jan, IRV elects C like all of the other methods if the B faction doesn't truncate. But IRV elects A when the B faction truncates. Of course, with this knowledge, the B faction isn't likely to truncate, and as you say C will be elected. The trouble with IRV is that in the other scenario when the B faction truncates sincerely because of detesting both A and C, IRV still elects A instead of B. Date: Sat, 6 Aug 2011 11:46:12 -0600 From: Jan Kok To: Jameson Quinn , Election Methods Mailing List Subject: Re: [EM] Chicken problem (was: SODA and the Condorcet criterion) To review for other readers, we're talking about the scenario 48 A 27 CB 25 BC Candidates B and C form a clone set that pairwise beats A, and in fact C is the Condorcet Winner, but under many Condorcet methods, as well as for Range and Approval, there is a large temptation for the 25 B faction to threaten to truncate C, and thereby steal the election from C. ?Of course C can counter the threat to truncate B, but then A wins. ?So it is a classical game of chicken. Some methods like IRV cop out by giving the win to A right off the bat, so there is no game of chicken. Wait a minute! IRV elects C in this scenario, if that is how the voters actually vote, and those are the sincere preferences (A voters have no preference between B and C). Much as I hate to say it, IRV works OK in that scenario. On the other hand, if the A voters prefer B over C, (as in the 2009 Burlington, VT mayoral election, http://scorevoting.net/Burlington.html) IRV ignores the preference and still elects C, which seems to be the wrong choice. -- ___ Election-Methods mailing list Election-Methods@lists.electorama.com http://lists.electorama.com/listinfo.cgi/election-methods- electorama.com End of Election-Methods Digest, Vol 86, Issue 18 Election-Methods mailing list - see http://electorama.com/em for list info
[EM] AQ variant of DSC
One way of looking at Woodall's DSC method is that it is designed to elect from
the clone set that
extends up to the top rank on the greatest number of ballots, i.e. kind of the
plurality winner among
clone sets.
There are two ways in which this description is not precise, but maybe we would
get a better method if
we follwed this description more closely.
(1) The solid coalitions look like clone sets on the ballots that reach up to
the top, but they don't have to
look like clone sets on the other ballots.
(2) This description doesn't tell how DSC narrows down after finding the
plurality winner solid coalition.
In fact the entire set of candidates is automatically the solid coalition that
extends to the top rank on
100% of the ballots, so for starter we need to narrow down to a proper
sub-coalition.
With regard to (1), imagine a one dimensional issue space with the candidates
distributed as follows:
A..B1..B2..B3...C..D1..D2...E
The set {B1, B2, B3} and the set {D1, D2} will be solid coalitions that
extend to the top rank on the
ballots of the voters that have a favorite among them, and they will appear as
clone sets on all of the
ballots that do not rank C first. But voters near C may well intermingle the
B's and the D's like
C B3D1B2D2B1EA
This shows that a geometrical clone doesn't have to end up as a classical
ballot clone except on the
ballots of the voters that are situated in the middle of the clone set, in
which case they will appear as
solid (or assenting) coalitions that extend to the top rank.
So Woodal had the right idea for making his method clone independent.
If I uderstand correctly, Woodall invented DSC to prove a point, viz. that a
method can satisfy later no
harm, be clone free, and montone. He didn't invent the method as a serious
proposal. So I don't think
his feelings will be hurt if we suggest an improvement.
My suggestion is that once we have found the proper subset solid coalition that
extends to the top rank
on the greatest number of ballots, strike from the ballots the candidates that
are not in that coalition, and
iterate until there is only one candidate left. Elect the sole remaining
candidate.
For incomplete rankings we can modify DAC in the same way, by replacing the
term solid with the
term assenting.
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Re: [EM] Chicken problem (was: SODA and the Condorcet criterion)
On 6.8.2011, at 19.40, Jameson Quinn wrote: More thoughts on the chicken problem. Again, in Forest's version, that's a scenario like: 48 A 27 CB 25 BC C is the pairwise champion, but B is motivated to truncate, and C to retaliate defensively, until A ends up winning. In my opinion, scenarios like this make the single most intractable practical strategy problem in voting theory: Approval, Range, and median-based systems all suffer directly. Most winning-vote-like Condorcet systems fall prey, including otherwise-great systems like Schulze. Margins systems have no truncation incentive - but as a direct consequence, they give extremely difficult-to-justify results if the B block truncates; in fact, they allow a strategic C block to fool the system into thinking it's seeing this scenarion when actually B and C are mortal enemies. IRV does relatively well with this scenario - but in return, pays no attention at all to the second choice of the A voters, which should be decisive if it exists. At the other extreme, some systems resolve this problem by forcing strict rankings from the A voters - but if they really don't have a preference, that ends up being just statistical noise, and doesn't even necessarily remove the game-of-chicken incentives if things are balanced right. Moreover, forcing B and C voters into strict rankings only makes them escalate their truncations into burials. Most of us, when we want to test our voting systems with a difficult case, use a strict-ranking Condorcet cycle of three; the old, standard ABC BCA CAB scenario. That's nice and simple, but not very realistic. To me, the game of chicken scenario; the resulting Condorcet cycle if B truncates; and related scenarios that could strategically be made to masquerade as these; are better practical tests for a voting system. In fact, I'd go so far as to guess that a real-life Condorcet cycle would be more likely to be the result of playing chicken than of honest preferences. As Forest already explained, SODA, as currently formulated, resolves the game of chicken — if all votes are delegated. It can do that because games among finite candidates are much more tractable than those among oceans of voters. SODA's sequential trick would be ridiculous with voters; imagine Your turn to vote is on Sunday at 2:35:58 PM. In my previous message in this thread (Re: SODA and the Condorcet criterion), I pointed out that there's still a problem if voters explicitly truncate by refusing to delegate. But I've been considering this issue, and eventually I found a solution that I think is simple enough to include in SODA: Make all candidate's predeclared rankings into strict rankings by breaking declared ties in order of the current approval totals when it's their turn to use their delegated votes. So if B voters truncated, candidate A would see that B was headed for a win, and would have the option to delegate to C. All the truncation would have accomplished would be to make A into a kingmaker between B and C. Since A could have had this kingmaker power, if she had wanted it, from the start, that's not a problem. The only difference between this end-game kingmaker power of A's, and if she had simply declared a preference from the start, is that the end-game power could in theory arise no matter which of B or C has more approvals, whereas an initial preference would only confer kingmaker power if the preferred candidate ended up with fewer approvals. Is this version of SODA really the only system to have a fully-satisfactory resolution to the chicken problem? Even if it is, is it worth adding this additional complexity to SODA? Can anyone make a chicken-like scenario which still stumps this SODA version? (If your scenario has more than 4 candidates, please use DAC instead of approval to find the SODA order of play.) Or do you know of a different system which creatively resolves the chicken problem? Remember trees :-). In a tree where B and C form one branch they and their voters are bound to support each others. Juho JQ 2011/8/5 Jameson Quinn jameson.qu...@gmail.com 2011/8/5 fsimm...@pcc.edu Jameson, as you say, it seems that SODA will always elect a candidate that beats every other candidate majority pairwise. If rankings are complete, then all pairwise wins will be by majority. So at least to the degree that rankings are complete, SODA satisfies the Condorcet Criterion. Also, as I mentioned briefly in my last message under this subject heading, SODA seems to completely demolish the chicken problem. Well almost. See below. To review for other readers, we're talking about the scenario 48 A 27 CB 25 BC Candidates B and C form a clone set that pairwise beats A, and in fact C is the Condorcet Winner, but under many Condorcet methods, as well as for Range and Approval, there is a
Re: [EM] : Chicken problem (was: SODA and the Condorcet
2011/8/6 fsimm...@pcc.edu Jan, IRV elects C like all of the other methods if the B faction doesn't truncate. But IRV elects A when the B faction truncates. Of course, with this knowledge, the B faction isn't likely to truncate, and as you say C will be elected. The trouble with IRV is that in the other scenario when the B faction truncates sincerely because of detesting both A and C, IRV still elects A instead of B. Also, if the A faction votes AB, then B clearly should win, but does not under IRV. So yes, IRV solves the chicken dilemma, but in so doing causes other problems. (This same argument, as it happens, works against tree-based methods.) I still claim that SODA is the only system I know of that can solve the chicken dilemma without over-solving it and making other problems. Election-Methods mailing list - see http://electorama.com/em for list info
