Re: [EM] IRV ballot pile count (proof of closed form)
If you object to plurality as I used it below, then WHAT label would you use for this major (often used) election method? I did go to Robert's 10th which is not into our level of detail on this topic (I see neither approval nor Condorcet mentioned). I went to Wikipedia, which I see as agreeing with what I wrote as to all three categories. On Feb 13, 2010, at 4:33 PM, Abd ul-Rahman Lomax wrote: At 11:55 PM 2/11/2010, Dave Ketchum wrote: We all get careless and stumble, sooner or later! But I choke on two details here: You misuse the label plurality - having only the ability to vote for 1 even though, for many races most intelligent voters will find there is only one candidate deserving approval. Even Approval has more power, letting voters vote for more than one, though unable to differentiate. Condorcet is another important step up, letting voters vote for more than one while indicating which they like best. Forcing voters to act as if they wanted to vote for more than they wish to is a step backward, and should not pretend to be an asset for a method. I'm not following Mr. Ketchum's arguments here. But plurality was used in a very ordinary sense. Any method which elects without a vote of a majority of those who cast non-blank ballots in an election is an election by plurality, using the definitions of Robert's Rules (and of most parliamentary procedure manuals, I believe, if not all). There is room for interpretation on whether or not a non-blank ballot that does not contain a legal vote should be included in the basis for majority, but no room for excluding from the basis those who do cast a valid vote, but for a candidate that is, say, later eliminated due to low vote count. Hence almost all voting systems that have been considered, absent vote coercion (as with mandatory full ranking or penalization of partial ranking, as happens with some versions of Borda Count), are plurality methods, including Approval and Range and, the point here, Condorcet methods. I did incorrectly state the case at first, by showing lower rankings that did add additional votes for other candidates by A. The example was clearer with all bullet votes. What this points out is that a ranking of, say, ABCDDFGH is, from this point of view, a vote for G over H. Should this be considered an approval of G? The voter has expressed that, in an election between G and H, the voter would prefer H, though, in fact, in a deep ranking like that, this is probably noise for the most part. (Robson Rotation is, in fact, used to eliminate some of this noise by averaging it out so that, at least, it is not produced by ballot position.) Majority is a word whose merits need more serious thought - see an earlier post from today. Ditto runoffs. Your words below seem intended as response - but I see little if anything as to merits. Dave Ketchum Indeed. Voting systems theory, early on, focused on attempts to find the ideal single-ballot system, from various perspectives. While this is a theoretically interesting question, it essentially misled the entire field when applied to real election reform, ignoring the most widely used voting reform, top two runoff, as if it were merely a more expensive and cumbersome version of Sri Lankan Contingent vote. Or batch-elimination IRV, same thing. It isn't. It produces different results than IRV, in about one-third of runoffs in nonpartisan elections. (Probably in partisan elections, it produces roughly the same results.) In addition, this approach ignored the *universally used* direct democratic method, repeated balloting, with no decision being made without a majority of those voting supporting it. None. No exceptions. Ignoring explicit voter approval, then, is one of the widespread systemic errors. Another one, arising early on, was the assumption that pure preference profiles were adequate to understand how voting systems would amalgamate votes and produce a useful social ordering, when, in fact, any sane method of studying how voting systems work would realize that a strong preference is different from a weak or barely detectable one, not to mention an indistiguishable one that is forced by a voting system to be crammed into one of AB or BA, with no allowance for A=B. And real, human, social decision-making systems, outside of voting, do consider preference strength, very much. And any system that attempts to maximize benefit to a society based on preference profiles would have to take preference strength into account. That it may be difficult to do this, that it may be difficult to determine commensurability, does not change this. What we can see through the device of assuming absolute utilities for voters in simulated elections is that the Condorcet Criterion and the Majority Criterion, for similar reasons, can require preposterous results, in situations
Re: [EM] IRV ballot pile count (proof of closed form)
2010/2/10 Abd ul-Rahman Lomax a...@lomaxdesign.com At 02:16 PM 2/10/2010, Jameson Quinn wrote: What if the bribe is payable only after the vote, and only for effective votes? (And don't say that the bribegiver can't be trusted. Since corruption is often a very cheap investment for the bribegiver, they would not be particularly motivated to fail to pay the bribe after the fact. Even if trust was lacking, human ingenuity can easily come up with ways of securing the deal.) The real issue is whether or not it would be easier to corrupt a delegable proxy system than others. Although you make a number of other, speculative arguments for why DP should be objectively difficult to corrupt, this is by far your strongest point. Even if DP is corruptible - an idea which, despite your arguments, I still find plausible - I see no reason why it should be more corruptible than any present-day system, or than any other proposed system. Any anti-corruption safeguards could be made to work as well or, in some cases, better under DP than with other systems. Thus, corruptibility is not really a valid argument against DP. (In other words... quit while you're ahead. If you have one good argument, you don't need 3.) Jameson Quinn Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] IRV ballot pile count (proof of closed form)
At 01:08 PM 2/10/2010, Dave Ketchum wrote: Condorcet does an N*N matrix showing for EACH pair of candidates which is better liked - used in counting and usable by others to help plan their future. Often there is a CW which wins for winning in all of its pairs; else a cycle in which each would be CW if other cycle members were not candidates. How best to resolve a cycle is debatable, but a simple method could be used unless others are demonstrated to be much better: Delete weakest pair used to define the cycle; repeat until remainder defines a CW. Note that N*Ns show progress, or lack of such, among non-winners. Often overlooked is that Condorcet methods, if truncation is allowed (and voting without truncation being allowed tends to input a lot of noise), is that it they are plurality methods, unless used with special rules, which I've never seen anyone buy myself propose. Consider the following votes: 34 A 33 BC 33 CB. The Condorcet winner is A, because in the two pairwise elections involving A, A wins AB, 34:33 AC, 34:33. However, A certainly does not have a majority. This is a problem entirely apart from the issue of cycles. Note that a majority winner is always a Condorcet winner. In the election above, almost two-thirds of the voters are actually voting against A. A could be a *lousy* result. Or not. Can't tell. I just noticed that while Wikipedia has many articles on voting systems, it doesn't list as a voting system what is commonly used by democratic organizations, probably most commonly! Repeated ballot until a majority is found for the winner. No eliminations, the election process is repeated, with new nominations allowed -- and, of course, withdrawals are also allowed. Basically, seeking a majority and not insisting on finding a winner in a single ballot, can make Condorcet almost irrelevant. (But I find it quite relevant in determining featured candidates in runoff elections; in my view, a Condorcet winner should *always* be, if not the winner, at least featured in a runoff election, for optimal overall results. But some algorithms may make a runoff unnecessary, i.e., the possible improvement in social utility from holding a runoff *might* be so small as to make it unnecessary. And I'd vastly prefer much more collection of data on real elections that do collect much more information than is on a plurality ballot, than coming to some fixed conclusion about that, snatched out of thin air.) Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] IRV ballot pile count (proof of closed form)
Consider the following votes: 34 A 33 BC 33 CB. The Condorcet winner is A, because in the two pairwise elections involving A, A wins AB, 34:33 AC, 34:33. Huh? I count 66 voters who prefer either B or C over A. Change it up: 49 A 26 BC 25 CB Now the CW is B. In the C vs. B competition, 26 pro-B voters beat 25 anti and 49 indifferent voters. This is arguably problematic, but not nearly as pathological as the original example would have been if true. The pro-(BC) coalition has decided the relative worth of B and C, while the A voters have abstained on that question. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] IRV ballot pile count (proof of closed form)
Abd wrote: 34 A 33 BC 33 CB. The Condorcet winner is A, because in the two pairwise elections involving A, A wins AB, 34:33 AC, 34:33. Assuming that by the above votes you mean 34:AB=C 33:BCA 33:CBA, A is not the Condorcet winner and is in fact the Condorcet loser, losing both A:B and A:C by 34:66. Perhaps you had in mind an example like 35:A 32:BC 33:C, by which I mean 35:AB=C 32:BCA 33:CA=B. In this example, C is the Condorcet winner even though C does not have a majority over B. I can see how this example could be seen as an embarrassment to the Condorcet criterion, in that a good method might not choose C as the winner. -- Rob LeGrand r...@approvalvoting.org Citizens for Approval Voting http://www.approvalvoting.org/ Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] IRV ballot pile count (proof of closed form)
At 01:45 PM 2/11/2010, Abd ul-Rahman Lomax wrote: 34 A 33 BC 33 CB. The Condorcet winner is A, because in the two pairwise elections involving A, A wins AB, 34:33 AC, 34:33. Oops. Of course, A is the Condorcet loser. I added the second preferences as an afterthought. I meant 34 A 33 B 33 C But more examples could be constructed where there is deeper ranking. Why bother, though? Condorcet methods, like any deterministic single-ballot method, is a plurality method, unless voters are coerced into voting for candidates they do not wish to be responsible for supporting, as with mandatory full ranking. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] IRV ballot pile count (proof of closed form)
We all get careless and stumble, sooner or later! But I choke on two details here: You misuse the label plurality - having only the ability to vote for 1 even though, for many races most intelligent voters will find there is only one candidate deserving approval. Even Approval has more power, letting voters vote for more than one, though unable to differentiate. Condorcet is another important step up, letting voters vote for more than one while indicating which they like best. Forcing voters to act as if they wanted to vote for more than they wish to is a step backward, and should not pretend to be an asset for a method. Majority is a word whose merits need more serious thought - see an earlier post from today. Ditto runoffs. Dave Ketchum On Feb 11, 2010, at 9:02 PM, Abd ul-Rahman Lomax wrote: At 01:45 PM 2/11/2010, Abd ul-Rahman Lomax wrote: 34 A 33 BC 33 CB. The Condorcet winner is A, because in the two pairwise elections involving A, A wins AB, 34:33 AC, 34:33. Oops. Of course, A is the Condorcet loser. I added the second preferences as an afterthought. I meant 34 A 33 B 33 C But more examples could be constructed where there is deeper ranking. Why bother, though? Condorcet methods, like any deterministic single-ballot method, is a plurality method, unless voters are coerced into voting for candidates they do not wish to be responsible for supporting, as with mandatory full ranking. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] IRV ballot pile count (proof of closed form)
At 05:33 AM 2/10/2010, Kristofer Munsterhjelm wrote: Abd ul-Rahman Lomax wrote: Who says organization, says oligarchy. One has to be careful not to have the organization become undemocratic, because the default tendency is for it to turn so, since it is (initially) more effective that way. That's right. The Iron Law of Oligarchy. Nice Wikipedia article on it, last time I looked. Oligarchy is inevitable and necessary, but the trick is to contain it and keep it responsible, to members who have means to be informed, information that is generally trustworthy, and who retain as much individual power as possible. Yes, it's quite likely that they will stay this course right into the ground. Hitching proportional representation (a very good idea) on to single-winner STV (a quite bad idea) may have seemed like a good idea at the time, perhaps because of the brilliant invention of the name, instant runoff voting, which itself suggested a strategy to spread the idea by attacking a vulnerable institution, but it was, in fact, not sustainable. Some of the reasons why it is not sustainable were not necessarily known then. Who would have expected that IRV would closely imitate Plurality in nonpartisan elections? Lots of people seem to be surprised that IRV doesn't produce real majorities, but that one was known. I think there's somewhat of an improvement no matter how small aspect to it, as well. IRV handles the spoiler problem with minor third parties, woo hoo! and then they stop there. But how much of that is after-the-fact justification (means for the ends that is STV) and how much of that is truly believed is hard to tell. The original goal still exists for FairVote, but has largely been eaten by the IRV monster. That the preceding organizations to FairVote co-opted the PR movement was noticed early on, by the original PR proponents. If Richie realizes the problems, he doesn't let on. He's a dedicated, bulldog political activist, and, in general, I consider his office to be part of the problem. It's necessary in an adversarial system, far less so in systems that attempt to find social consensus. And the prior history of IRV in the U.S. should have been a clue. What was it replaced with? Often -- not always -- with top two runoff. Because of the desire for majorities For multiwinner STV, you could argue that the reason it was replaced was not because it did so badly, but because it did too well. Consider New York. After STV, there were many parties, not just the Democratic stranglehold. What did the Democrats do, seeing their power being diluted? Since they didn't want to share, they started employing red-scare tactics, with such rational appeals as calling the method Stalin Frankenstein. Yes. The same is true, by the way, with Bucklin. It worked; when it failed' it had simply reverted closer to Plurality due to bullet voting. As for IRV, the single-winner method, you're probably right. In some situations, the reason is that it seems to provide no different results than Plurality. In others, there's complexity (which is made no better by that IRV isn't summable). FairVote has sold IRV most successfully in jurisdictions that were using top-two runoff with nonpartisan elections, and in that environment, it's clear that dropping TTR for IRV is quite equivalent, in practice, to simply running Plurality, which is a lot cheaper. I have seen one fairly clear exception, the Ed Jew District 4 Supervisor race in San Francisco in 2006, and in that race, we had visible markers (the names of the candidates) that identified ethnic affiliation, apparently quite similar to partisan affiliations in partisan elections. It stands out like a sore thumb in the vote transfers, and apparently Jew actually only campaigned to Asians and advised them to rank all the Asian candidates. Since the district has a high Asian population So this exception actually proves the rule. Nominally non-partisan, but, in fact, highly partisan. Top Two Runoff is an improvement over Plurality, and is the most-established election reform in the U.S. And FairVote has been shooting it down with its efforts. It's tragic, in fact. In the long run, though, it will probably prove to have been suicidal, as results from all these trials accumulate and are analyzed by people who aren't nailed to the FairVote agenda. Well, Asset bypasses the whole shebang, by making what we think of as elections irrelevant. At least in theory. Everyone wins in an Asset election, or, if not, then there is someone very specific for the voter to blame: the candidate the voter voted for in first preference. (Asset may be STV with the Asset tweak for exhausted ballots, or it could just be vote-for-one. I, personally, would see no need or desirability to rank more candidates, provided my choice has a backup (a proxy should be allowed in case of incapacity), but some people seem to think otherwise.
Re: [EM] IRV ballot pile count (proof of closed form)
I've elsewhere detailed how an attempt to corrupt a proxy in a DP system could easily lead to a mouthful of hair for the would-be corrupter. They pay the money, they get the open support of the proxy, the proxy ends up looking very good to the constituents, who, on this issue, vote directly, bypassing the proxy's vote. I've recommended in DP systems that proxies *not accept* votes from large numbers of constituents, or, at least, that they understand the problems created if they do. If I got large numbers of requests to serve, I would instead recommend that they choose someone who has chosen me. And then I can communicate with all of them through direct (and private) communication with a handful of individuals. So I've been offered some huge sum to exercise my influence. Publicly, I promote the idea, using the best arguments provided to me, and perhaps I shut up about the reasons why it's a Bad Idea. But I'm in direct communication with my set of direct clients, and we discuss everything, routinely. And it would be very easy to make sure that they are aware of the counterarguments and that I'm voting as I vote because of, shall we say, special considerations. So I vote and argue as I'm paid to do, and my clients decide that they just don't like my opinion on this particular issue, so they vote directly. What if the bribe is payable only after the vote, and only for effective votes? (And don't say that the bribegiver can't be trusted. Since corruption is often a very cheap investment for the bribegiver, they would not be particularly motivated to fail to pay the bribe after the fact. Even if trust was lacking, human ingenuity can easily come up with ways of securing the deal.) Consider the common types of corruption at the moment. The two most common are non-quid-pro-quo support for the candidate who, of themselves, are more amenable to one's position, unless both are on one's side (this is corrupt if the issue is under the radar for most voters, as it tends to winnow opposition down to nothing over time, even if the majority of the electorate opposes you); and allowing lobbyists essentially free hand in writing the fine print of laws (again, the point is that the average voter will not know or care enough about the effects of this to make a difference). If the majority - even an overwhelming majority - does not care enough to vote directly, then it can be perfectly effective to corrupt the judgement of a key representative. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] IRV ballot pile count (proof of closed form)
At 02:16 PM 2/10/2010, Jameson Quinn wrote: What if the bribe is payable only after the vote, and only for effective votes? (And don't say that the bribegiver can't be trusted. Since corruption is often a very cheap investment for the bribegiver, they would not be particularly motivated to fail to pay the bribe after the fact. Even if trust was lacking, human ingenuity can easily come up with ways of securing the deal.) The real issue is whether or not it would be easier to corrupt a delegable proxy system than others. Question about a payment for effective votes? Do you mean an actual decision that favors the bribegiver, or merely that the bribegiver does his best, as far as the bribegiver sees? Now, if I were doing something illegal, like accepting a bribe, I'd have no trust in being able to enforce an agreement. I've never heard of a bribe being payment on results; in addition, I might corrupt myself, place all my relationships at risk, and then, because the arguments for this proposal were bad, it doesn't pass. That my own clients might also betray my vote and open argument is only part of this. If I don't tell my clients and I argue stupid arguments to them, then I risk my entire relationship with them. It better be a lot of money! Remember, I'm not suggesting DP for government, per se. The political applications would be for organizations that advise voters. So what a bribe would be accomplishing is that I'd give bad advice to voters. In a DP system, this really means to my friends. That's sociopathic. Now, how many sociopaths are going to be highly trusted, in a system that depends on frequent personal contact (not the abstract persona and image that play in present politics)? And the trust runs in both directions. If a proxy has weak connections with clients, say, lots of clients, they will not be as solidly advised, they may take it or leave it. They won't donate money to a suggested cause, they won't necessarily bother to vote. Consider the common types of corruption at the moment. The two most common are non-quid-pro-quo support for the candidate who, of themselves, are more amenable to one's position, unless both are on one's side (this is corrupt if the issue is under the radar for most voters, as it tends to winnow opposition down to nothing over time, even if the majority of the electorate opposes you); and allowing lobbyists essentially free hand in writing the fine print of laws (again, the point is that the average voter will not know or care enough about the effects of this to make a difference). If the majority - even an overwhelming majority - does not care enough to vote directly, then it can be perfectly effective to corrupt the judgement of a key representative. That's right. That's how corruption works. Rather than spend money to serve the public more effectively to win contracts, spend money to influence a corrupt award. It only makes sense if there is some fulcrum, some point of serious excess power. You are incorrect about one thing. It's not necessary for the majority to vote on most things. In an Asset system, most people, the vast majority, would vote once every election cycle, for a representative. It's possible that there may be different reps: to neighborhood, to city, to county, to state. Those who are more interested will offer to serve as electors and register as candidates. These become public voters and will be far more motivated than your average citizen, and probably substantially more knowledgeable, on average. Anyone can do it, in the systems I envision, but getting other people, enough to make it worth the continued effort, isn't so easy. Still, none of it is lost, the votes aren't wasted. You just pass it on, and, in a direct/Asset rep system, you can either forget about it -- which then makes your rep like a present rep -- or you can watch -- or you can watch closely only when there is an issue you have some particular interest in. And when you have something to say about it, you know exactly whom you can go to, *your representative*. The one you gave your votes to. You will be recieved, I expect, with more genuine cordiality than we are accustomed to from our representatives. Remember, you freely picked this person as the one you most trust to pass on your votes to. (If this person also passed your vote on, that merely gives you *two* people to go to.) To me, Asset Voting is not merely an election method, it is a device for increasing involvement in government, for making the connection between the people and government very real, tangible, visible, as well as fair. We are so far from this that it's hard for most of us to imagine. *OUR government.* I've been in a small town where it was like that. Town Meeting government, in fact. Sure, there were elected officials, but the town was actually run by the people, and it felt like that. Positions were volunteer except for
Re: [EM] IRV ballot pile count (proof of closed form)
At 12:20 PM 2/8/2010, Kristofer Munsterhjelm wrote: Abd ul-Rahman Lomax wrote: Given that much better methods exist, have been tried and worked, and are much easier to canvass, WTF? If I were to guess: in part a desire to produce a stepping stone to STV, and in part organizational inertia. FairVote bet on IRV and now will stay the course. That's right. One of my first observations on this, when I became aware of the election methods list and the Approval voting list, and discovered the Center for Voting and Democracy, which had started as the Center for Proportional Representation, and which became FairVote, was that people trying to reform democracy didn't trust democracy, they would always gravitate toward nondemocratic institutions which are easily co-opted to become self-preserving and inflexible. Typical co-opt is by staff! Yes, it's quite likely that they will stay this course right into the ground. Hitching proportional representation (a very good idea) on to single-winner STV (a quite bad idea) may have seemed like a good idea at the time, perhaps because of the brilliant invention of the name, instant runoff voting, which itself suggested a strategy to spread the idea by attacking a vulnerable institution, but it was, in fact, not sustainable. Some of the reasons why it is not sustainable were not necessarily known then. Who would have expected that IRV would closely imitate Plurality in nonpartisan elections? Lots of people seem to be surprised that IRV doesn't produce real majorities, but that one was known. And the prior history of IRV in the U.S. should have been a clue. What was it replaced with? Often -- not always -- with top two runoff. Because of the desire for majorities To address the former: the grail here would be a polytime monotone summable multiwinner method that reduces to a good Condorcet variant (or Bucklin/Range/etc) in the single-winner case. A multiwinner method can be summable in two ways: summable with the number of seats held fixed, or summable no matter what. Well, Asset bypasses the whole shebang, by making what we think of as elections irrelevant. At least in theory. Everyone wins in an Asset election, or, if not, then there is someone very specific for the voter to blame: the candidate the voter voted for in first preference. (Asset may be STV with the Asset tweak for exhausted ballots, or it could just be vote-for-one. I, personally, would see no need or desirability to rank more candidates, provided my choice has a backup (a proxy should be allowed in case of incapacity), but some people seem to think otherwise. I'd rather not yank my vote away from my most-trusted candidate to put it in the hands of this less-trusted candidate, but then to return it to the most trusted if the less-trusted drops out somehow. rules in STV/Asset have not much been delineated.) What's important is that we don't know of such a method; but also that the stepping stone strategy itself might be dangerous - if the base method is bad, then it may fail to dislodge those whose interest is in less democracy, and so the objective of moving to multiwinner never gains any additional strength by the so-called stepping stone. My own decision about all this is that it's best to begin with NGOs, voluntary organizations that demonstrate how advanced methods work. The Election Science Foundation held an Asset election for its steering committee. It was quite interesting Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] IRV ballot pile count (proof of closed form)
On Feb 6, 2010, at 12:27 AM, Kristofer Munsterhjelm wrote: For all practical purposes, except when there are only a few candidates, the first format (1) would be much more compact than the second - which is the point you're making. The data is probably quite compressible as well. Well, yes. So why bother with opaque binary formats? Choose a natural text representation of the ballots, add a digital signature, and compress the result. For linear ballots, each ballot is just a list of candidates, or candidate keys (A,B,etc) with a key-to-name table added. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] IRV ballot pile count (proof of closed form)
Abd ul-Rahman Lomax Sent: Friday, February 05, 2010 4:50 PM CUT Practically speaking, I'd assume, the precincts would be provided with a spreadsheet showing the possible combinations, and they would report the combinations using the spreadsheet, transmitting it. So some cells would be blank or zero. With 5 candidates on the ballot, the spreadsheet has gotten large, but it's still doable. What happens if preferential voting encourages more candidates to file, as it tends to do? 23 candidates in San Francisco? Even with three-rank RCV, it gets hairy. Respectfully, I would suggest this would NOT be a wise way to collect the data. As I pointed out in my e-mail that correctly listed the maximum possible number of preference profiles for various numbers of candidates, the actual number of preference profiles in any election (or any one precinct) with a significant number of candidates, will be limited by the number of voters. Further, because some (many) voters will choose the same profiles of preferences, the actual number of preference profiles will likely be even lower - as in the Dáil Éireann election I quoted. Thus a spreadsheet containing all possible preference profiles would be unnecessarily large and the probability of making mistakes in data entry would likely be greater than if each precinct recorded only the numbers for each profile actually found in that precinct. CUT There is a way to avoid such massive reporting, which is to report interactively, which is what is done in Australia. Only one set of totals is reported from a precinct at a time, the totals for the current round. (which can be just uncovered votes due to eliminations that have been reported to the precinct from central tabulation.) However, the problem with this is that a single error in a precinct can require, then, all precincts to have to retabulate. Yes, this distributed counting would work. But there is an even simpler solution - take all the ballots to one counting centre and then sort and count only the ballots that are necessary to determine the winner (or winners in an STV-PR election). That what has been done for public elections in Ireland and the UK for many decades and it works well without problems. But I do appreciate that is far too simple and practical a solution and it suffers from NMH. James Gilmour No virus found in this outgoing message. Checked by AVG - www.avg.com Version: 9.0.733 / Virus Database: 271.1.1/2669 - Release Date: 02/05/10 07:35:00 Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] IRV ballot pile count (proof of closed form)
At 01:12 PM 2/5/2010, James Gilmour wrote: Abd ul-Rahman Lomax Sent: Friday, February 05, 2010 4:50 PM CUT Practically speaking, I'd assume, the precincts would be provided with a spreadsheet showing the possible combinations, and they would report the combinations using the spreadsheet, transmitting it. So some cells would be blank or zero. With 5 candidates on the ballot, the spreadsheet has gotten large, but it's still doable. What happens if preferential voting encourages more candidates to file, as it tends to do? 23 candidates in San Francisco? Even with three-rank RCV, it gets hairy. Respectfully, I would suggest this would NOT be a wise way to collect the data. As I pointed out in my e-mail that correctly listed the maximum possible number of preference profiles for various numbers of candidates, the actual number of preference profiles in any election (or any one precinct) with a significant number of candidates, will be limited by the number of voters. Further, because some (many) voters will choose the same profiles of preferences, the actual number of preference profiles will likely be even lower - as in the Dáil Éireann election I quoted. That's correct; however, there is no practical way to predict which profiles are needed. Sorting the ballots into piles and subpiles until there is a separate pile for every profile strikes me as how it would be done. (or they could be sorted in sequence, according to the physical position of the marks, which would be faster, probably). Then the data from each pattern would be entered into the matching position on the spreadsheet. Thus a spreadsheet containing all possible preference profiles would be unnecessarily large and the probability of making mistakes in data entry would likely be greater than if each precinct recorded only the numbers for each profile actually found in that precinct. The probability of making mistakes is not as stated, because there is a check on the spreadsheet data, there can be several checks. First of all, I'd first sort the ballots by first preference and transmit that data. This is merely preliminary, but those totals might decide the election. The sums should equal the number of ballots found. Then the piles would be sequenced and the totals for each particular pattern found. It may be more efficient to keep A.B separate from AB, because there is less interpretation required. I.e., Blank simply becomes another candidate. That adds to the possibilities, for sure, but simplifies the actual sorting. Blank intermediary votes should be pretty rare with IRV, so this will not materially add to the data that must be transmitted. The spreadsheet could be transmitted raw, or it could be edited to remove empty rows (i.e, patterns with no ballots found matching). That reduces transmitted data but increases local processing and possibility for error. However, in either case, the check by summing remains. The check for subpatterns of each first choice is an additional error check. The first data transmitted could actually be used to shorten the process, i.e., there would be two reports from precincts: the first report with only first rank votes, a wait for central tabulation to have collected enough precincts to be able to advise on batch elimination, and then an additional transmission with all remaining relevant patterns There is no doibt but that IRV can be counted, but the point is that it can get really complex and take a lot of time, when an election is close with many candidates. With more than a small handful of candidates, experience has shown that it can be a time-consuming and expensive process, done by hand. And very difficult to audit, even if done by computer. That's why the election security people here in the U.S., in general, don't like it. What is done, in practice, is to collect and analyze ballot images. This has been done with preprocessing to collapse votes like A,B, but that's actually only a minor improvement and reduces transparency. If I'm correct, the collection of the data has been done centrally, the equipment not being present at the voting precincts, so, in short, they truck the ballots to central tabulation. This creates other risks. However, the problem with this is that a single error in a precinct can require, then, all precincts to have to retabulate. Yes, this distributed counting would work. But there is an even simpler solution - take all the ballots to one counting centre and then sort and count only the ballots that are necessary to determine the winner (or winners in an STV-PR election). That's what's being done. What experience here shows is that, even centrally counted, errors happen in earlier rounds that then require recounting all later rounds. The possibility of this rises with the number of candidates and the closeness of the election. That what has been done for public
Re: [EM] IRV ballot pile count (proof of closed form)
On Feb 4, 2010, at 7:51 PM, Kathy Dopp wrote: The general formula for the number of possible rankings (for strict ordering, without allowing equal rankings) for N candidates when partial rankings are allowed and voters may rank up to R candidates (N=R if voters are allowed to rank all candidates) on a ballot is given on p. 6 of this doc: http://electionmathematics.org/ucvAnalysis/US/RCV-IRV/ InstantRunoffVotingFlaws.pdf the only issue, Kathy, is whether the lower limit is i=0 or i=1. you have to defend your use of i=0 for the case illustrated below (using the rules in Burlington VT and Cambridge MA). In the US, R=3 in most IRV elections. in Burlington it was 5 in both 2006 and 2009. N was also 5 (not counting any write-in). but Kathy, suppose N=R=3 and it's the regular-old IRV rules that do not require any minimum number of candidates ranked and do not allow ties. to be clear, i need to also point out that only *relative* ranking is salient (at least in Burlington). if a voter only ranks two candidates and mistakenly marks the ballot 1 and 3, the IRV tabulation software will close up the gaps and treat that precisely as if it was marked 1 and 2. now, given those parameters, are you telling us that the 9 tallies shown on Warren's page: http://rangevoting.org/Burlington.html (i have very similar numbers, no more different than 4), are not sufficient to apply the IRV rules and resolve the election? 1332 MKW 767 MWK 455 M 2043 KMW 371 KWM 568 K 1513 WMK 495 WKM 1289 W is there any reason those 9 tallies could not have been summed from subtotals coming from all 7 wards of Burlington? please tell us why those 9 piles are not enough, given the parameters stated above? -- r b-j r...@audioimagination.com Imagination is more important than knowledge. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] IRV ballot pile count (proof of closed form)
On Feb 4, 2010, at 8:29 PM, Kathy Dopp wrote:
On Thu, Feb 4, 2010 at 8:18 PM, robert bristow-johnson
r...@audioimagination.com wrote:
On Feb 4, 2010, at 7:51 PM, Kathy Dopp wrote:
The general formula for the number of possible rankings (for strict
ordering, without allowing equal rankings) for N candidates when
partial rankings are allowed and voters may rank up to R candidates
(N=R if voters are allowed to rank all candidates) on a ballot is
given on p. 6 of this doc:
http://electionmathematics.org/ucvAnalysis/US/RCV-IRV/
InstantRunoffVotingFlaws.pdf
the only issue, Kathy, is whether the lower limit is i=0 or i=1.
you have
to defend your use of i=0 for the case illustrated below (using
the rules in
Burlington VT and Cambridge MA).
False Robert. Starting the index at 0 or 1 is completely irrelevant.
so you're saying that
N-1 N-1
SUM{ N!/i! } = SUM{ N!/i! } ?
i=0 i=1
that the N!/0! term is equal to zero?
Any formula is easily adjusted to either initial index.
i ain't talking about any substitution of dummy variable, i, and
changing the limits.
You are obviously not a mathematician.
i guess not. just a Neanderthal electrical engineer who does signal
processing algs for a living.
in Burlington it was 5 in both 2006 and 2009. N was also 5 (not
counting
any write-in).
My formula gives the general case for R equals anything, as I said.
but Kathy, suppose N=R=3 and it's the regular-old IRV rules that
do not
require any minimum number of candidates ranked and do not allow
ties. to
be clear, i need to also point out that only *relative* ranking is
salient
(at least in Burlington). if a voter only ranks two candidates and
mistakenly marks the ballot 1 and 3, the IRV tabulation software
will close
up the gaps and treat that precisely as if it was marked 1 and 2.
So? What's your point?
the point is that a ballot marked with 1 and 3 goes on the same pile
as a properly marked ballot marked with the same two candidates as
1 and 2.
now, given those parameters, are you telling us that the 9 tallies
shown on
Warren's page:
http://rangevoting.org/Burlington.html (i have very similar
numbers, no
more different than 4), are not sufficient to apply the IRV rules and
resolve the election?
Obviously you did not read my email. I'll read and respond to yours
after you've tried to read and understand my points. Otherwise I am
not wasting my time responding to you.
no need to, but...
1332 MKW
767 MWK
455 M
2043 KMW
371 KWM
568 K
1513 WMK
495 WKM
1289 W
is there any reason those 9 tallies could not have been summed from
subtotals coming from all 7 wards of Burlington?
please tell us why those 9 piles are not enough, given the
parameters stated
above?
... you're running away from the salient question. are those 9 piles
good enough to resolve the IRV election with 3 candidates or not?
was salient information lost when the MK pile was combined with the
MKW pile, enough that could cause the IRV election (with the rules
above) to be decided differently?
--
r b-j r...@audioimagination.com
Imagination is more important than knowledge.
Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] IRV ballot pile count (proof of closed form)
Kathy Dopp wrote: People on this list seem to still be sending around their incorrect or incomplete formulas for the number of possible rank orders for rank order ballots. This number BTW does *not* correspond to the number of piles needed to count IRV which is a lesser number but does correspond to the only method of making IRV precinct-summable. For precinct summability, whether or not you include both AB and ABC votes as distinct (in a three-candidate election) doesn't really matter because the factorial term dominates and so one can broadly say: - When one formula says it's practical to send raw ballot counts around, it's practical to do it by any of the other formulas - When not practical for one, it's not practical for the others either. Of course, when verifying the outcomes, you'd want to have the exact number right, but it seems to me that the question of whether the method can be feasibly summed in precincts by transmitting raw counts (how many voted this order, how many voted that order) does not depend on the exact nature of the formula, because they all grow so quickly. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] IRV ballot pile count (proof of closed form)
robert bristow-johnson wrote:
On Feb 2, 2010, at 2:28 PM, robert bristow-johnson wrote:
Warren tells me that
C-1
SUM{ C!/n! }
n=1
has a closed form, but didn't tell me what it is. does someone have
the closed form for it? i fiddled with it a little, and i can
certainly see an asymptotic limit of
(e-1)(C!)
as C gets large, but i don't see an exact closed form for it. if
someone has such a closed form, would you mind sharing it?
Okay, I spent a little time working on this and figgered it out. The
fact that the number of distinct piles needed to represent all possible
manners of *relatively* ranking C candidates (no ties except unranked
candidates are tied for lowest rank) is
C-1
SUM{ C!/n! } = floor( (e-1) C! ) - 1
n=1
Now I wonder if there's a closed form for the number of orders with both
equality and truncation permitted. Since I don't quite get the proof, I
can't answer, though!
Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] IRV ballot pile count (proof of closed form)
On Feb 2, 2010, at 2:28 PM, robert bristow-johnson wrote:
Warren tells me that
C-1
SUM{ C!/n! }
n=1
has a closed form, but didn't tell me what it is. does someone
have the closed form for it? i fiddled with it a little, and i can
certainly see an asymptotic limit of
(e-1)(C!)
as C gets large, but i don't see an exact closed form for it. if
someone has such a closed form, would you mind sharing it?
Okay, I spent a little time working on this and figgered it out. The
fact that the number of distinct piles needed to represent all
possible manners of *relatively* ranking C candidates (no ties except
unranked candidates are tied for lowest rank) is
C-1
SUM{ C!/n! } = floor( (e-1) C! ) - 1
n=1
I was at first unconvinced that the right hand side is an exact
closed form for the left, but now accept that it is.
The proof requires as given:
inf
SUM{ 1/n! } = e ~= 2.718281828...
n=0
The floor(a) function which returns the only integer such that
a-1floor(a) = a
and, if n is an integer, then
floor(a + n) = floor(a) + n for any a.
It also requires knowledge that if C and n are integers and C = n, then
C!/n! = C(C-1)(C-2)(C-3)...(n+1) = integer
From that
inf C-1inf
C! e = SUM{ C!/n! } = C! + SUM{ C!/n! } + C!/C! + SUM
{ C!/n! }
n=0 n=1 n=C+1
or
C-1inf
C! e = C! + SUM{ C!/n! } + 1 + SUM{ C!/n! }
n=1 n=C+1
The first three terms on the RH are integers. The last term
inf
SUM{ C!/n! } = 1/(C+1) + 1/[(C+1)(C+2)] + 1/[(C+1)(C+2)(C+3)]
+ ...
n=C+1
is less than
inf
SUM{ C!/n! }1/C + 1/C^2 + 1/C^3 + ...
n=C+1
which is
infinf
SUM{ C!/n! }(1/C) SUM{ (1/C)^j } = (1/C)/[1 - (1/C)] =
1/(C-1)
n=C+1 j=0
which is less than 1 for any C 2. So we know that the last term in
C-1inf
C! e = C! + SUM{ C!/n! } + 1 + SUM{ C!/n! }
n=1 n=C+1
is less than 1.
Then applying the floor() function to both sides yields
C-1inf
floor(C! e) = floor( C! + SUM{ C!/n! } + 1 + SUM{ C!/n! } )
n=1 n=C+1
which is
C-1 inf
floor(C! e) = C! + SUM{ C!/n! } + 1 + floor( SUM{ C!/n! } )
n=1 n=C+1
Since the argument of the floor() function on the right is less than
1, the returned value of the floor() function is known to be zero.
C-1
floor(C! e) = C! + SUM{ C!/n! } + 1
n=1
Resulting in
C-1
SUM{ C!/n! } = floor( (e-1) C! ) - 1
n=1
at least for any integer C greater than 2.
I do this kinda thing all the time at comp.dsp or the music-dsp
mailing list, but haven't done this before outside of those two
technical contexts.It was kinda fun.
Thanks Warren, for the hint.
--
r b-j r...@audioimagination.com
Imagination is more important than knowledge.
Election-Methods mailing list - see http://electorama.com/em for list info
