[Election-Methods] Ballots with cycles
Suppose that in a Condorcet system, we allow people to submit a ballot that has an arbitrary preference relation, so any two alternative A and B can have either AB. There can therefore be cycles in the graph of preferences, like Ahttp://electorama.com/em for list info
Re: [Election-Methods] Ballots with cycles
In ranking systems we think of the voter assigning a numeric rank to each candidate such as, for A,B, 4,5 or 4,4 or 5,4. What are you proposing? Remember also that in a race for governor the voting information must go to a central counting site. In Condorcet, without your proposal, the information for each precinct can be entered in an array and forwarded, with the arrays summed to get total votes. DWK On Wed, 5 Mar 2008 07:54:12 -0500 Andrew Myers wrote: > Suppose that in a Condorcet system, we allow people to submit a > ballot that has an arbitrary preference relation, so any two > alternative A and B can have either AB. There can > therefore be cycles in the graph of preferences, like A > One reason why we might want to set up the system this way is that we > can protect voter privacy better by separating different preferences > during the tallying process. > > The question is whether this creates new strategic voting > opportunities. I have not been able to construct a scenario where it > makes strategic voting more powerful. Is this worse than burying > with ordinary ranked ballots? > > -- Andrew -- [EMAIL PROTECTED]people.clarityconnect.com/webpages3/davek Dave Ketchum 108 Halstead Ave, Owego, NY 13827-1708 607-687-5026 Do to no one what you would not want done to you. If you want peace, work for justice. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [Election-Methods] Ballots with cycles
On Mar 5, 2008, at 14:54 , Andrew Myers wrote: > Suppose that in a Condorcet system, we allow people to submit a > ballot that has an arbitrary preference relation, so any two > alternative A and B can have either AB. There can > therefore be cycles in the graph of preferences, like A > One reason why we might want to set up the system this way is that we > can protect voter privacy better by separating different preferences > during the tallying process. I don't think this makes much difference. It is also ok to separate a regular linear opinion A>B>C to three separate binary preferences A>B, A>C and B>C. And in both cases the typical way to carry the results forward from the first place where the votes are locally counted is in a form of a pairwise matrix, so the ballots can be packed, sealed and stored locally if needed. Normally we assume that voters are rational in the sense that they can set a personal preference order to the candidates. With this assumption the possibility of giving arbitrary preference relations is of no use to sincere voters. > The question is whether this creates new strategic voting > opportunities. I have not been able to construct a scenario where it > makes strategic voting more powerful. Is this worse than burying > with ordinary ranked ballots? This makes it a bit easier to intentionally generate a loop among say three candidates (A,B,C) of the competing party. My vote could be X>A, X>B, X>C, A>B, B>C, C>A, where X is my own party candidate. If many X supporters vote systematically this way there is a chance that the candidates of the competing party will all lose to each others, and that might make X the winner in some Condorcet methods like minmax if the race is otherwise very tight between the two parties. Use of arbitrary preferences is interesting but rather theoretical, and the changes in the outcome might be marginal (at least in typical public elections). Any more reasons why it should be allowed? (In regular public elections also the complexity of the ballots might be a show stopper.) (If different ballots have different complexity that might be a risk to voter privacy (you would cast a complex vote while most other votes would be simpler).) Juho > -- Andrew > > Election-Methods mailing list - see http://electorama.com/em for > list info ___ Inbox full of spam? Get leading spam protection and 1GB storage with All New Yahoo! Mail. http://uk.docs.yahoo.com/nowyoucan.html Election-Methods mailing list - see http://electorama.com/em for list info
Re: [Election-Methods] Partisan Politics
Yes, agreed. In addition to having some targets on improving the society politicians (and any human beings) are often interested (to a varying degree) also in power, money and fame. Politics can offer all this to them. Another problem is that all aging "systems" have the risk of stagnation and gradual corruption. You mentioned also the problem of people believing that their own and dear system is already the best possible. And (as you also noted) the incumbents in good positions in the current system have no interest in changing the system (since that system was the one that gave them their current position). Improving such a system is always an uphill battle. I note that the financing of the campaigns may be a serious problem. One could try to do something with that also without the proposed method (e.g. by setting some limits on TV time and/or newspaper rows and/or number of phone calls and/or letters). Fraud is also a serious problem. In this case I do believe that also the current systems can be made practically fraud free, if there is just some political will to do so. (One just needs to make the ballots and process clear and count the results locally in the presence of representatives from multiple interest groups and then make the results public.) Few notes on the "Selecting Leaders From The People" method. The first possible theoretical problem is the fact that electing one candidate from each group to some extent favours large groups. I make a simplifying assumption that also in the new system there are two parties with 55% and 45% support. I also assume that a group that has two or three representatives from one party always elects a a candidate from that party. As a result the probability of electing a candidate from the bigger party is higher than 55%. And when one repeats this procedure multiple times hierarchically, eventually almost all representatives would be from the bigger party. My assumptions simplified the set-up a lot, but the trend of favouring large groupings is there. I don't know if this is ok to you or not. The basic idea that representatives at one layer will be elected by representatives at one step lower layer makes the gap between voters and representatives smaller than what it typically is today, and thereby makes the relationship stronger (this has many good implications). One can achieve these effects also with larger groups and fewer layers. One extreme is the electoral college in US that reduces the number of steps in two (I don't claim that it would have the same properties though). Another slightly different approach would be to elect not one but several representatives at each layer. This would reduce the problem of favouring large groupings. A similar tree style hierarchy could be constructed e.g. from groups of 1000 voters electing 50 representatives for the next higher layer. Also this hierarchy still favours large groupings but to a lesser degree. (This method would be in style more like a multi-winner multi-party method.) I wonder if the groups of three (or more) always represent some specific region. I guess this was the intention. I.e. if the process starts at the backyard will it also continue to electing the representatives of neighbourhoods, towns etc. If so, that would probably make the ties between the representatives and their voters tighter. If the relationship is tight and will be about the same also in the next elections that would make the representatives one step more responsible towards their voters (=> leads to some sort of a "village chief/representative" system). One problem is that even if the process, when started from a backyard, has no party influence at the beginning, it is possible that the party influence will infiltrate the system from top down (in good and bad). I.e. if there are some groupings/parties at the top level, the candidates at one level below could make their affiliations clear, and their voters might request them to do so. And that could then continue downwards in chain. The long chain in decision making is likely to lead also to complaints that the highest level decision makers do not listen to the lowest level voters any more, and that thers is some sort of corruption "in the chain". Maybe the chain should not be too long. And in some elections (or part of them) voters might also like to elect their representative directly. (For example how should one elect a president of a mayor? Maybe direct voting would be used in some cases instead of the chained voting model.) The practical problem of making the politicians adopt this proposal is of course huge. But one must start somewhere. Making people aware of the problems and offering them also good solutions to the problems may some day lead to small steps forward. Juho On Mar 4, 2008, at 23:54 , Fred Gohlke wrote: Good After
Re: [Election-Methods] Ballots with cycles
Juho wrote: > > Use of arbitrary preferences is interesting but rather theoretical, > and the changes in the outcome might be marginal (at least in typical > public elections). Any more reasons why it should be allowed? > > (In regular public elections also the complexity of the ballots might > be a show stopper.) > (If different ballots have different complexity that might be a risk > to voter privacy (you would cast a complex vote while most other votes > would be simpler).) Juho, Thanks for your thoughts on this. The reason to have it is that you can take a ballot that is expressed as ordinary rankings and decompose it into a set of individual preference relationships, each of which does not reveal much information about the voter. The various preferences are still summable, but preferences coming from different voters can be mixed together, preserving their privacy. This addresses a vulnerability sometimes called the "Italian attack" or "Sicilian attack", legendarily associated with some elections in that region (I have no actual evidence that this really happened!), in which voters could be identified by the precise rankings used in their ballots, dictated by party bosses. With N alternatives, the N! possible orderings can uniquely identify many voters. The concern is that a voter might be able to inject a set of preferences into the system that do not correspond to any numeric ranking, if they control the software is that generates the preference relationships. So the question is whether there is a scenario in which a voter doing this is able to swing an election that cannot be swung by a voter who only generates transitive orderings. -- Andrew Election-Methods mailing list - see http://electorama.com/em for list info
Re: [Election-Methods] Using range ballots as an extension of ranked ballot voting
At 03:20 PM 3/2/2008, [EMAIL PROTECTED] wrote: >I'm curious about voting methods that take ranked ballot methods and >adapt them to range ballots. For example, with Baldwin's method, you >take drop the candidate with the lowest Borda score, recalculate, >and so on. A range variant might drop the candidate with the lowest >range score, normalize the remaining scores, and repeat. It should >still give the Condorcet winner (if any) but it might fit different >election criteria than standard Baldwin. Likewise, a range >generalization of the Kemeny-Young order might be interesting. There is a fundamental problem with ranked methods, which is that ranking neglects preference strength. You can take a Range ballot and analyze it as a ranked ballot, and derive some useful information, but the reverse is problematic. Borda runs into problems because of the assumption of equal preference gaps. Borda *is* a kind of Range, but with that assumtion, which is, quite simply, not reflective of the real world. Range works, at least in theory, because preference strength *is* important, particularly to the only reasonable method of election performance that I'm aware of, social utility (making the assumption that the full range of satisfaction of each voter is as worthwhile as the full range of satisfaction of every other voter; the common objection about non-interpersonal-comparability of utilities is based on ignoring this assumption, which is pretty much fundamental to democracy.) I've proposed that, in fact, Range ballots be analyzed as ranked ballots, pairwise. I've never fully specified a method, but the basic idea is that if the Range winner is beaten by another candidate, pairwise, there is an actual runoff election. One of the realizations I've come across in the last year is that runoff elections test preference strength, that the claim that runoffs are unfair is probably incorrect. Real top-two runoffs seem to reverse the vote in about one-third of the cases, from my examination of a limited number of such elections; but IRV, so far, isn't generating that reversal, and there is very strong preservation of preference order in each IRV round. The plurality winner is the final winner, and the runner up is still the runner up, and it goes deeper than that in some of these many-candidate elections in San Francisco. Replacing Top-two runoff with IRV is practically insane. With very few exceptions, the IRV winner still did not get a majority of the votes cast in the election, and it is only by discarding exhausted ballots -- that contained valid votes -- that an apparent majority appears. This is entirely contrary to the principle of requiring a majority in the first place, which is why top-two was being used to start with. Given that IRV seems to be almost always choosing the plurality winner, why not stick with Plurality? Or a method more likely to find a true majority. (IRV is sometimes declaring a winner who *does* have a majority, but it's concealed underneath other active preferences.) Some of the San Francisco IRV elections generated enough data to do Bucklin analysis, and Bucklin did find a majority more often, from the same votes. Same results, of course. But a heck of a lot cheaper to count And it was used for a long time in the U.S., and was apparently popular. Anyway, Range with runoff as I described would be uncontestably Majority Criterion compatible. It can detect Range failure due to voter misapprehension of the true situation, correcting for strategic voting. I think it's a really interesting idea Smith's simulations found Range with runoff to be better at S.U. maximization than pure range, probably due to normalization error. That was simply top-two runoff Range, no pairwise analysis was performed, but almost always, if there is a pairwise winner over the Range winner, that candidate would, in fact, be the Range runner-up. Another modification of Range is to explicitly define an approval cutoff, and require a runoff if the winner isn't approved by a majority. Same with Approval voting, actually. Should require a majority to win (and a double majority, the situation where Approval allegedly fails the majority criterion, is not a majority choice, and a runoff fixes the problem. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [Election-Methods] Ballots with cycles
Let's look at Condorcet: Voter ranks as many candidates as wished, assigning each of them a rank. Counter records in an array with one row and one column for each candidate. For each pair of ranked candidates, calling the higher ranked A, and the other B, count in row A, column B. For each pair of ranked candidate A and unranked candidate B, count in row A, column B. The array contains nothing but the total counts for all the ballots in the precinct. The ballots have no further purpose to serve. Does not seem possible for your proposal to make the ballots less identifiable. Does not seem practical for your additions to be useful: They seem more difficult to use than normal. If they, somehow, give a voter extra power, seems like they should be forbidden. DWK On Wed, 5 Mar 2008 19:17:06 -0500 Andrew Myers wrote: > Juho wrote: > >>Use of arbitrary preferences is interesting but rather theoretical, >>and the changes in the outcome might be marginal (at least in typical >>public elections). Any more reasons why it should be allowed? >> >>(In regular public elections also the complexity of the ballots might >>be a show stopper.) >>(If different ballots have different complexity that might be a risk >>to voter privacy (you would cast a complex vote while most other votes >>would be simpler).) > > Juho, > > Thanks for your thoughts on this. > > The reason to have it is that you can take a ballot that is expressed as > ordinary rankings and decompose it into a set of individual preference > relationships, each of which does not reveal much information about the > voter. The various preferences are still summable, but preferences > coming from different voters can be mixed together, preserving their > privacy. This addresses a vulnerability sometimes called the "Italian > attack" or "Sicilian attack", legendarily associated with some elections > in that region (I have no actual evidence that this really happened!), > in which voters could be identified by the precise rankings used in > their ballots, dictated by party bosses. With N alternatives, the N! > possible orderings can uniquely identify many voters. > > The concern is that a voter might be able to inject a set of preferences > into the system that do not correspond to any numeric ranking, if they > control the software is that generates the preference relationships. So > the question is whether there is a scenario in which a voter doing this > is able to swing an election that cannot be swung by a voter who only > generates transitive orderings. > > -- Andrew -- [EMAIL PROTECTED]people.clarityconnect.com/webpages3/davek Dave Ketchum 108 Halstead Ave, Owego, NY 13827-1708 607-687-5026 Do to no one what you would not want done to you. If you want peace, work for justice. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [Election-Methods] Ballots with cycles
Thanks. I missed the part of breaking the ballot into pieces already before counting it. I know one example where at least people claimed that one person monitoring the elections in a small village, after watching all the voters vote, after the day had almost accurate results on how many votes each candidate got (there were numerous candidates). I think with this kind of good understanding of the local people one could guess whose ballot some ballot is if one would see the detailed content of the ranking (or rating) based more complex ballots. One approach to fixing this is to increase the size of the lowest level vote counting areas, e.g. from minimum size of 50 to minimum size o 500. This may depend also on the number of candidates. One aspect that may reduce the problems is that people may rank only a limited set of the candidates. But of course they are not guaranteed to do so. One rather radical way to make the votes more unidentifiable would be to simply allow the voters to mark only n candidates, or use only m ranking categories for all of them. A bad example case might be one where I vote: MyBrother>MyFriend>MyNeighbour>MyPartyMember1>MyPartyMember2. If some of the people close to me and my friends would be one of the vote counters he/she could with reasonable certainty check that all in the "team of friends" voted as expected. Another bad example is to ask someone to vote WeirdCandidate1>WeirdCandidate2>MrX>... and another one WeirdCandidate7>WeirdCandidate6>MrX>... This would allow MrX to buy votes or coerce voters. The weird candidates are marked just to make the ballots recognizable (they have no chances of winning the race). They could as well be at the end of the ballot (to avoid the risk of them getting elected). So, if one wants to avoid all this one could mandate (not only allow) the voters (or the voting machine) to cut their votes into smaller two-candidate relationships already before dropping the vote into the ballot box. On the other hand one should still make sure that everyone casts only one vote and doesn't e.g. drop two A>B ballot fragments into the box. Because of all the complexity this could maybe be best done by a machine. The voter would just mark ordinary preferences and then the machine would cut the vote into small vote fragments and drop them into the box. And if this is done by the machine there would again be no compelling need to allow circular votes (hard enough to guess the original linear votes from the fragments). One could in this case as well allow only linear votes but still break them into intraceable fragments. Juho On Mar 6, 2008, at 2:17 , Andrew Myers wrote: > Juho wrote: >> >> Use of arbitrary preferences is interesting but rather >> theoretical, and the changes in the outcome might be marginal (at >> least in typical public elections). Any more reasons why it should >> be allowed? >> >> (In regular public elections also the complexity of the ballots >> might be a show stopper.) >> (If different ballots have different complexity that might be a >> risk to voter privacy (you would cast a complex vote while most >> other votes would be simpler).) > Juho, > > Thanks for your thoughts on this. > > The reason to have it is that you can take a ballot that is > expressed as ordinary rankings and decompose it into a set of > individual preference relationships, each of which does not reveal > much information about the voter. The various preferences are still > summable, but preferences coming from different voters can be mixed > together, preserving their privacy. This addresses a vulnerability > sometimes called the "Italian attack" or "Sicilian attack", > legendarily associated with some elections in that region (I have > no actual evidence that this really happened!), in which voters > could be identified by the precise rankings used in their ballots, > dictated by party bosses. With N alternatives, the N! possible > orderings can uniquely identify many voters. > > The concern is that a voter might be able to inject a set of > preferences into the system that do not correspond to any numeric > ranking, if they control the software is that generates the > preference relationships. So the question is whether there is a > scenario in which a voter doing this is able to swing an election > that cannot be swung by a voter who only generates transitive > orderings. > > -- Andrew ___ Copy addresses and emails from any email account to Yahoo! Mail - quick, easy and free. http://uk.docs.yahoo.com/trueswitch2.html Election-Methods mailing list - see http://electorama.com/em for list info
Re: [Election-Methods] Ballots with cycles
I missed one case. The votes can be made more anonymous by allowing only a limited number of candidates, or using ballots that contain complete rankings only if the number of candidates happens to be small enough. Typical presidential elections might e.g. have only say five candidates and the number of different possible ballots could be small enough (301 I think) to avoid losing privacy if the number of votes counted in one location is large enough. (Note that also simple ballots that are used today may allow many tricks. Ballots with extra markings may be deemed invalid but still it is possible e.g. to write the marks in a certain recognizable way. Machine voting, and maybe not using even machine made paper ballots or record of original ballots at all, would make things easier, but of course could lead to some other kind of vulnerabilities. Well, I guess the elections should be made "good enough to be trusted enough".) Juho On Mar 6, 2008, at 8:30 , Juho wrote: Thanks. I missed the part of breaking the ballot into pieces already before counting it. I know one example where at least people claimed that one person monitoring the elections in a small village, after watching all the voters vote, after the day had almost accurate results on how many votes each candidate got (there were numerous candidates). I think with this kind of good understanding of the local people one could guess whose ballot some ballot is if one would see the detailed content of the ranking (or rating) based more complex ballots. One approach to fixing this is to increase the size of the lowest level vote counting areas, e.g. from minimum size of 50 to minimum size o 500. This may depend also on the number of candidates. One aspect that may reduce the problems is that people may rank only a limited set of the candidates. But of course they are not guaranteed to do so. One rather radical way to make the votes more unidentifiable would be to simply allow the voters to mark only n candidates, or use only m ranking categories for all of them. A bad example case might be one where I vote: MyBrother>MyFriend>MyNeighbour>MyPartyMember1>MyPartyMember2. If some of the people close to me and my friends would be one of the vote counters he/she could with reasonable certainty check that all in the "team of friends" voted as expected. Another bad example is to ask someone to vote WeirdCandidate1>WeirdCandidate2>MrX>... and another one WeirdCandidate7>WeirdCandidate6>MrX>... This would allow MrX to buy votes or coerce voters. The weird candidates are marked just to make the ballots recognizable (they have no chances of winning the race). They could as well be at the end of the ballot (to avoid the risk of them getting elected). So, if one wants to avoid all this one could mandate (not only allow) the voters (or the voting machine) to cut their votes into smaller two-candidate relationships already before dropping the vote into the ballot box. On the other hand one should still make sure that everyone casts only one vote and doesn't e.g. drop two A>B ballot fragments into the box. Because of all the complexity this could maybe be best done by a machine. The voter would just mark ordinary preferences and then the machine would cut the vote into small vote fragments and drop them into the box. And if this is done by the machine there would again be no compelling need to allow circular votes (hard enough to guess the original linear votes from the fragments). One could in this case as well allow only linear votes but still break them into intraceable fragments. Juho On Mar 6, 2008, at 2:17 , Andrew Myers wrote: Juho wrote: Use of arbitrary preferences is interesting but rather theoretical, and the changes in the outcome might be marginal (at least in typical public elections). Any more reasons why it should be allowed? (In regular public elections also the complexity of the ballots might be a show stopper.) (If different ballots have different complexity that might be a risk to voter privacy (you would cast a complex vote while most other votes would be simpler).) Juho, Thanks for your thoughts on this. The reason to have it is that you can take a ballot that is expressed as ordinary rankings and decompose it into a set of individual preference relationships, each of which does not reveal much information about the voter. The various preferences are still summable, but preferences coming from different voters can be mixed together, preserving their privacy. This addresses a vulnerability sometimes called the "Italian attack" or "Sicilian attack", legendarily associated with some elections in that region (I have no actual evidence that this really happened!), in which voters could be identified by the precise rankings used in their ballots, dictated by party bosses. With N alternatives, the N! possible orderings can uniquely identify many voters. The concern is that a voter might be able to inject a set
