Re: [EM] Bouricius reply, BR, Tideman, recent USA elections
Tideman said IRV was unsupportable if it is feasible to compute pairwise matrix. That was because Tideman had other voting methods he considered clearly superior to IRV and these methods used the pairwise matrix.By clearly superior I mean, so superior in every respect, that Tideman felt there was no conceivable use for IRV, ever (in situations where it was feasible to compute pariwise matrix) where that use could be supported. That is what unsupportable means. Tideman ranks IRV highest in resistance to strategy, and generally better than the pairwise methods in lucidity and cost of computation. How does that translate to those methods being superior in every respect? --I should have said superior OR THE SAME in every respect, with some superiorities. One method (which is almost the same as but appears better than one advocated by Tideman) which I call WBS-IRV is as follows. WBS-IRV: votes are rank-orderings. While a beats-all winner does not exist, repeatedly eliminate the candidate with the fewest top-rankings. This has about the same score as IRV on Tideman's strategy resistance and also probably better score on J.Green-Armytage's strategy vulnerability probability. It has the same properties as IRV among those considered by Tideman (note Tideman does not consider later no harm as worth mentioning...) except better in some ways e.g. it elects Condorcet winners. It is equally simple. -- Warren D. Smith http://RangeVoting.org -- add your endorsement (by clicking endorse as 1st step) and math.temple.edu/~wds/homepage/works.html Election-Methods mailing list - see http://electorama.com/em for list info
[EM] NESD and NESD* properties of a single-winner voting method
To formalize something pretty well known by now as a property: A single-winner voting system fails the NESD property if, when every honest voter changes their vote to rank A top and B bottom (or B top and A bottom; depends on the voter which way she goes), leaving it otherwise unaltered, that always (except in very rare exact tie situations) causes A or B to win. Presumably voting systems failing NESD will generally lead a country into 2-party domination. Systems failing NESD: IRV (instant runoff voting), plurality, and all Condorcet systems. By these I mean, with pure-rank-order ballots (no rank-equalities permitted). Systems passing NESD: Borda, approval and range voting. However: Borda restricted to 3-candidate elections fails NESD. If we modify IRV to permit rank equalities by counting a ballot with K candidates co-equal top as 1/K votes for each, then this system passes NESD, although I still feel uncomfortable about it because being co-equal top is plainly a lot worse and more vulnerable than being sole-top (there is kind of a discontinuity, unlike in range voting where it is continuous as you cross the top score), so strategic voters might not do the former. To make an analogy, plurality voting with equal votes permitted (i.e. you can vote half for Jefferson and half for Adams) would clearly be stupid, i.e. would clearly be essentially equivalent strategically to plain plurality. Consider each of your half-votes one at a time. If for the first, your best move was to vote Jefferson, then for the second, the same reasoning would apply. Hence you'd vote 100% for Jefferson and never use the equality feature (unless you were a strategic idiot). But anyway, Plurality with equals permitted, does technically pass NESD. If we consider Condorcet systems with rank-equalities permitted, these pass NESD but again there is that worrying discontinuity. One might define the NESD* property to be the same as NESD except A and B are to be SOLE-top-rated or ranked by all voters. Then Fail NESD*: IRV, plurality, Condorcet (all with rank-equalities permitted or forbidden, both work). Pass NESD*: Range voting. NESD* not applicable: Approval voting. -- Warren D. Smith http://RangeVoting.org -- add your endorsement (by clicking endorse as 1st step) and math.temple.edu/~wds/homepage/works.html Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] About non-monotonicity and non-responding to previous posts...
Trying some fresh thinking for Condorcet, and what anyone should be able to see in the X*X array. I am ignoring labels such as Schulze and Ranked Pairs - this is human-doable and minimal effort - especially with normally having a CW and most cycles having the minimal three members. 1. Look at any pair of candidates. Loser is not the CW (there can be a tie in any comparison here - NOT likely in a normal election, but we have to be prepared with responses for such). 2. If there are other possible CWs, repeat step 1 with latest winner and one of them. 3. If there are other candidates latest winner has not been compared with, compare it with each of them. 4. If winner wins each of these, it is CW. 5. Winner and each who beat it in step 4 are cycle members. Also, any candidate beating any of these is also a cycle member. IF there is a CW, it should win - anything else is a complication, even if some math makes claims for the something else. Otherwise a simple cycle resolution should apply. Simply canceling the smallest margin has been thought of - that value means minimum difference in vote counts between actual and what is assumed. Note that each cycle member would be CW if remaining cycle members were ignored. As to voting: Equal ranks permitted. Write-ins permitted, and such a candidate wins with the same vote counts as if nominated. As to clones, strategy, primaries, and runoffs - all seem best ignored, though only a nuisance if some are determined to involve such. Dave Ketchum On Nov 8, 2009, at 6:33 AM, Kristofer Munsterhjelm wrote: robert bristow-johnson wrote: On Nov 5, 2009, at 1:35 PM, Kristofer Munsterhjelm wrote: robert bristow-johnson wrote: i don't think a sequence of elimination rounds would be okay, but the method of picking the biggest loser for each round needs to be debated. i am not sure what would be best. Are you referring to IRV here? no. i mean if there is a Condorcet cycle, as an alternative to Schulze or Ranked Pairs or whatever, you could start with the Smith Set and, with some meaningful metric, eliminate a candidate deemed to be the biggest loser, then rerun the superficial Condorcet tally (just see if there is a Condorcet winner among the candidates left) and repeat until a Condorcet winner is apparent from the candidates left over. I've been browsing old posts of this list, and I've encountered the idea or method of sprucing up, which may be of interest in this respect: http://lists.electorama.com/htdig.cgi/election-methods-electorama.com/2004-December/014372.html The relevant post for determining cycles is here: http://lists.electorama.com/htdig.cgi/election-methods-electorama.com/2004-December/014373.html and basically says that, in public elections, and in every election if the base method passes certain criteria, the question of how to resolve cycles can be reduced to drawing the borders of three regions of a triangle. The complexity of the question has thus been reduced quite a bit, even if it is now very abstract. On another note, Condorcet cycles don't have to be resolved through elimination. Also, there may be subsets of the Smith or Schwartz set, such as the uncovered (Landau, Fishburn) set, that have just one candidate even when the former sets have multiple, that can be used to resolve the cycles. Picking uncovered candidates confers protection against certain forms of strategy, as well. All of this is theoretical, since the methods are too clumsy for public proposal, but one has to start somewhere :-) You're right. If I were to guess, I'd say that in most situations, unless the electorate is small or uncertain, there will be a CW; however, once the method has been adopted, parties will try to coordinate strategies to induce a cycle, really? Terry B (also a Burlington resident) told me that, and i find that to be an untested hypothesis. since the parties do not know who will benefit from a cycle (who can tell the future?), i really have my doubts about that. They'll try, but that doesn't necessarily mean they'll succeed. If the method resists the initial strategy, they would eventually give up. In the case of STV, vote management did work (but it was very risky), and so the parties continued, adding noise to the system. I do think the good methods (River, MAM/Ranked Pairs, Schulze, etc) will manage to resist the initial attempts at coordinated strategy, but it does emphasize that you need some resistance to strategy in order to survive the metaphorical birth of fire. Some strategies could be maintained longer than others. Those that involve manipulation of the candidate set would be easier for a party than those that involve electoral strategy, for instance; so a method should be cloneproof (which the three I mentioned are), and should be independent of as many alternatives as possible (the three
Re: [EM] Anyone got a good analysis on limitations of approval andrange voting? (long)
Thanks all for the discussion and pointers. I still can't concretely conclude anything yet but here are some rambling and random thoughts based on what was said and my prior experiences. Plurality Leads to two lowest common denominator parties which are not accountable to the voters. This conclusion supported by real world observation. Feels right to the non-critical mind, one man, one vote Very fast at the polls Approval Encourages participation of minor parties and thus should keep the big guys paying attention to a wider base. Almost zero marginal implementation cost. Hanging chads count just fine :) Understandable by anyone but feels wrong at first not fair, you get more than one vote. Apparently has a terrible flaw but no one seems to be able to articulate it in layman terms. No real world experience available to illustrate the problem. Here is where I need to learn more. Data provided to date is unconvincing to me. Does not meet the desire of some to be able to differentiate between I like, I like a lot etc. (note: this seems like perfectionism to me. Large numbers of voters and opinions all over the bell curve should make individual expression at the greater level of granularity irrelevant.) Very fast at the polls. Pick yer favorites and head home for beer and telly. Range Can break the vicious cycle of plurality Not voting for someone at all can have a strong influence on election outcome. This is very non-intuitive and would take some getting used to. Allows for nuanced voting. Pain in the ass at the polls (relatively speaking). You can't safely disregard the candidates you don't care about so you *have* to assign everyone a ranking, possibly addressable by defaulting to zero for all candidates? This is considered a feature and I agree it has merit. But in reality it is a deal breaker for joe six pack and co. (and for lazy sobs like me). IRV Demonstrably broken. 'nuff said. Suite of complicated systems that strive to reach Condorcet ideals. No regular bloke would ever trust 'em because you can't explain how they work in one or two sentences. Technically superior to other systems. Not clear what problem with approval they would solve. Unless you are a perfectionist and insist that individuals express nuances of opinion... Some time ago I put together a site (primitive and unfinished[i]) to promote approval voting and in the process I spent a lot of time trying different systems on the web and repeatedly testing my own site. I noticed some interesting things from all that playing around. It was very uncomfortable to go back to plurality after trying other systems. It feels unfair and broken. It was very tedious voting in any of the ranking systems. Approval felt boring but good. I have checked in on this list now and then and I admit I don't have the time or skills to follow all the arguments but it strikes me that approval voting is good enough to break the deadlock, at least in US politics and that it doesn't have any major flaws. The very understandable desire to be able to articulate in a finer grained way in your vote is perfectionism. With millions of voters, for every person on the fence about a particular candidate there will be some to either side who will essentially make or break the vote. If you are on the fence, approve or disapprove, it won't matter. So, to re-frame my question. What is the fatal flaw with approval? I'm not interested in subtle flaws that result in imperfect results. I'm interested in flaws that result in big problems such as those we see with plurality and IRV. [i] www.approvalvote.org Election-Methods mailing list - see http://electorama.com/em for list info
