Hi, I am Mrprasad. I originally added the section "Condorcet Criterion Issue" a few days ago (i.e. 1-31-06; today is 2-3-06). A reader informed me that he was concerned that its use of the term "greatest possible consensus" was POV. I understood that concern and want to edit it in a manner that gets around this issue. However, I have not had the time to search for the necessary sources to back the claims. I do not feel I can rewrite the section without some reference to "greatest possible consensus". Thus, I feel the need to drop the section until I can better source the section. I will return it once I do that.

It is easily reversed as disapproval voting where a choice is disavowed, as is already required in other measures in politics (e.g. representative recall).

I don't see why approval voting is any different than any other system for "disapproval". The case cited (representative recall) is not even a single-winner contest. (throw all the bums out :-). It is a single-candidate contest if anything.... I propose dropping that text. NealMcB 18:10, 2004 Apr 29 (UTC)

Reads well now. The point about approval and preference voting both being single-vote systems is now there, but no hierarchy of 'this is a type of that' is anywhere in the descriptions of the voting systems themselves, which is fine, except for disapproval as a variant of approval, which seems the only clear inverse. 15:02, 2003 Jan 17

There was an earlier article here once, but it must have been censored.

Under Approval_voting#Potential_for_Tactical_voting I don't like this statement:

A good strategy is to vote for every candidate the voter prefers to the leading candidate, and to also vote for the leading candidate if he is preferred to the current second-place candidate. When all voters follow this strategy, the Condorcet winner is almost certain to win.

It is an opinion statement and I don't know what qualifications should be made for it. Who says this is a good strategy? How do we measure the "leading candidate"? Is that an approval measure or a plurality measure?!

I've done my own thoughts on Approval Voting and I judge:

A good strategy is to vote for the same candidate you would vote for in a plurality race, and also any candidates you prefer more (ignoring any assumption that those candidates can't win).

thus reducing the problem to the IMO harder one of deciding whom to vote for in plurality. --Townmouse 19:48, 16 Oct 2004 (UTC)

This stategy is more practical, and is MUCH more likely to be used, even if it doesn't help the Condorcet Winner.

It would merely allow weak candidates a fair measure of support (approval) without throwing the election against a preferred stronger candidate. Approval offers little to voters in a strong three-way race when the top leader is not predictable. Then approval is only useful as a maximal power "negative vote" against feared competitor(s). (Voting A=1,B=1,C=0 in approval is mathematically equivalent to A=0,B=0,C=-1)

I won't change anything for now, but I appreciate opinions. I accept the existing "good strategy" statement as "Good strategy to elect a Condorcet Winner".

Does anyone else have a problem with the existing "good strategy" statement? Any suggestions for changes?

Thanks! --Tomruen 00:02, 2 Jun 2004 (UTC)

The problem with your phrase is that the vote in a tactical vote in a plurality race may also depend on identifying the leading candidates in a plurality race, the leading candidates may be different under different rules and the information may not be avialable on how others might vote in a plurality race. For those who wish to vote in a way which is unlikely to affect the result, tactical voting advice is unnecessary, and I think the current text makes reasonable sense - the leading candidate obviously means in an approval measure. --Henrygb 23:16, 26 Jun 2004 (UTC)

Hmmm... my first assumption was "leading candidate" meant leading in a single-vote count since it is pretty much meaningless to poll voters with approval votes in a poll. Approval polling is too strongly open to manipulation, even unorganized manipulation - individuals playing around for fun or profit. I accept the same argument exists with single-vote counts, but people still want their true favorite to poll well and are less likely to play unless they really have no preference. --Tom Ruen 05:37, Jun 27, 2004 (UTC)

Surely a "good strategy" is a strategy that maximises that particular voter's expected utility. For a single-winner election that means one that maximises how much the voter likes the ultimate winner.

My question is why approval voting is single winner only. Is it called something else when the top n candidates are elected? --Henrygb 23:16, 26 Jun 2004 (UTC)

Approval certainly could be used for multiwinner elections and doesn't have or need any different name. In practice there's less reason to need it. The "standard" multiwinner election method is called Plurality-at-large or Bloc-voting which allows as many votes as candidates. It's less often people would want to "overvote" with multiple winners except as a defensive vote against one or more most disliked candidates. A more likely vote in plurality-at-large is voting for less candidates than winners because you don't want your lower choices to defeat higher ones.

Actually multiwinner Approval elections are an attractive idea - but only when candidates are truly evaluated independently - that is if the number of winners can be variable and the approval rating needed is fixed before the election.

For example a great application would be a poll for which ALL candidates with more than 15% approval are included in a presidential debate. That's a very valid poll since you know the more you vote for the more winners there will be and your vote for a second favorite CAN'T hurt the chances of winning for a first favorite. --Tom Ruen 05:37, Jun 27, 2004 (UTC)

Some thoughts:

• If Approval Voting had been in force in Florida 2000, then the mistakenly double marked ballots (for Gore and Buchanan) would still have counted. No votes would have been voided. Gore would have got all his genuine votes, while Buchanan was so far behind it would not have mattered it he got some bonus or unintended approval votes.

• Does Approval Voting comply with "one man one vote"? Yes it does, because any Buchanan votes do not really matter because he was so far behind, and Gore only ever recieves "one useful vote per voter".

• Has Approval Voting ever actually been used anywhere?

• The biggest disadvantage of Approval Voting may be that it distorts the election statistics - the total number of votes may appear to add up to more than 100%. Something would need to be done to "normalise" the results.

• If the votes in an Approval Vote contest add up to more than 100% turnout, how does convince the public that the election has not be tampered with? That might be a hard sell!

• If 999 Nader voters had approved of Gore, Gore would have beaten Bush.
• If 999 Buchanan voters had also approved of Bush, Bush would still have won.
• Note that there were 3rd Party candidates spoiling things on both sides.

Syd1435 09:23, 2004 Oct 4 (UTC)

Suppose one side of politics is a permanent Coalition, say City Republicans and Rural Republicans, and an election is being held using Approval Voting.

• If you do not mind which kind of Republican gets in, you approve of both kinds.

• But say for some reason or another, you would much prefer the Rural Republican to get elected - how then do you fill in your Ballot?

• Answer, you must approve of the RR candidate and disapprove of the CR candidate.

• Suppose there are other voters who prefer the City Republican candidate.

• Taken together, the two Republican candidates will lose a few votes compared to the sole Democratic candidate.

• There is thus a dangerous split in the Republican camp, albeit a modest one.

• This illustrates a flaw in Approval Voting, because all approvals have the same value, when in practice, some variation in the approval rating is desirable.

What is needed is some kind of intermediate approval level. Here is a sample ballot paper, to enable both Republicans to be approved, but with one preferred to the other. Then all Republican votes count toward beating the common enemy.

• [3] Joe Smith ----- Greens.
• [1] Henry Ford ---- Rural Republican
• [3] Jane Doe ------ Democrat
• [3] Fred Rubble --- Reform
• [2] Mary Hill ----- City Republican

Notes:

• [1] = 1st preference Approval (YES-FULL)
• [2] = 2nd preference Approval (YES-PART)
• [3] = Disapproval............ (NO)

Note that the Modified Approval Voting with variable levels of preference is starting to look like Instant Runoff Voting.

Put this the other way, Approval Voting is a restictive version of Instant Runoff Voting where instead of having N different ranks for N candidates, you are restricted to 2 different ranks for N candidates.

Hi Syd1435,

I'm moving your discussion of Approval voting's flaws to the talk page for two reasons (1) because it really looks like you're actively trying to plug IRV [instead of dispassionately describing the flaws in AppV] (2) the tone of the content is really a lot more conversational than it is encyclopedic. Let's work together to bring the most useful content from your contributions back to the article. Best, -- Kowey 08:55, 16 Oct 2004 (UTC)

P.S. I will confess that I am partial to AppV myself, so we should also get help from a more neutral 3rd party.

Since AV is also an abbreviation for Alternate Vote aka IRV, can we abbreviate Approval Voting as AppV?

I think it helps to compare FPTP, AppV and AltV aka IRV rather than dealt with them dispassionately on their own.

BTW, the 9 Oct Election is very exciting because preferential voting (IRV), slow absentee and postal ballots, mean that unexpected and interesting results are occurring. No point in having it all over on election night.

I am happy to work with you to get something acceptable back of article page.

Syd1435 12:10, 2004 Oct 16 (UTC)

• In an Approval Vote election, the total number of approvals will add up to more than 100% of the number of voters, which may appear to some people as a breech of the "One Man One Vote" principle. It is not a breech, but how does one argue that it is not a breech?

• Suppose that a voter approves of candidates B and C; but approves of candidate B more than C. How does he cast his votes?
  • If he approves of only B, the lack of an approval vote for C may let A in.
  • If he approves of both B and C, then he has failed to express his preference for B over C.
  • It is thus impossible to simultaneously approve of two candidates which preferring one over the other.
  • Approval voting suffers the disadvantage that all approvals are of equal weight, even when the vote wishes to express unequal approvals.

• These two problems are resolved with Instant Runoff Voting.
  • With IRV, the total number of votes for each candidate at every stage of the count equals the number of votes orignally cast.
  • If a votes put B first, C second and A third, then the full value of his vote is set against B in the first round. Depending on how B and C score against eachother, either the second preferences of C go to B, or the second preferences of B go to C. No votes need be lost in the struggle between like minded B and C against the common enemy A.
  • In military terms, there is no "Division of Force" when a voter preferences B before C. No matter whether a votes remains with its original choice, or is redistributed to a lower choice, that vote always retains its full value, one man, one vote, one value.

• There is a problem with Instant Runoff Voting that in practice is no longer a problem.
  • With Approval Voting, Limited Voting, and the like, when a computer is used to tally the results, only the total score for each candidate need be recorded. This requires only a small Commodure 64 computer with 64k of memory.
  • With Instant Runoff Voting, it is necessary to store an image of every ballot; it there are N ballots, and M candidates per ballot, then a Pentium computer with N * M bytes or even double bytes of memory is required.
  • It can also be represented with much less memory. Just as the example above represented many voters with just four columns, you can get my with just counting how many ef each *unique* ballot exists. You only need M * (M!) entries, each entry able to count up to N. For M=4 candidates, this comes to 96 entries. For M=10 candidates, this comes to about 36 mega-entries.
  • If Department of Elections only has Commodore 64 computers at its disposal, then a computerised IRV may be out of the question.
  • A computerised count of and IRV election would also take much more time to process than an Approval Voting election.
  • How many people still use Commodore 64 computers?

The Citizens for Approval Voting website uses the following ballot paper as its logo:

• • [YES] Jefferson - a great president
  • [NO ] Stalin - a tyrant
  • [YES] Madison - a great president
  • [YES] Washington - a great president

Clearly, it does not matter which of these three great presidents wins, so long as Stalin loses.

But suppose the ballot was revised as follows:

• • [YES] Jefferson - a great president
  • [NO ] Stalin - a tyrant
  • [YES] Madison - a great president
  • [ ? ] Warren G. Harding - a ROTTEN president

Now the choice is less clear. We would want even Warren G. Harding to beat Stalin, but either Jefferson or Madison to beat Harding. This example shows a fundimental weakness of Approval Voting. Cumulative Voting does better, and Instant Runoff Voting better still.

Put simply, Approval Voting cannot simultaneously approve of multiple candidates and choose between them.

An even more telling ballot would be to place Stalin against the three worst presidents.

Strategic or Tactical Voting occurs when a voter judges that their preferred candidate is not likely to win, and that therefore they are better off voting for a lesser of two evils candidate.

With FPTP, this can occur with three cornered contests. An unexpected third candiate can drain away enough votes to spoil victory for one of the leaders.

With Approval Voting, the drainage of votes is certain to be much less, since a voter can select both the original choice, as well as the lesser of two evils choice.

If however, the vote judges than their preferred candidate has a winning chance, they may decline to approve of the lesser of two evils choice, making room for the worst of two evils to get in, if they miscalculate. This could be gut-wrenching. Some voters will thus only approve of the preferred candidate and decline to support the lesser of two evils candidate, casting a FPTP like ballot.

With Instant Runoff Voting, the voter ranks their first choice first, the lesser of two evils candidate second, and the worst of all evils last. No combination or permutation of preferences can help elect the worst of all evils, assuming that the voter ranks all candidates. The need not be any leakage of preference that might spoil the result as a PFTP vote can do, or a AppV vote does to some extend.

When an IRV ballot is filled in, with all the candidates ranked consequtively from 1 to N, there can be no circular preferences, (A>B, B>C, C>A). Preferences always flow unambiguously D>A>E>B>C, etc.

With AppV ballot there are no circular rankings, but there are ambiguous rankings say (A=D=E)>(B=C).

With FPTP ballot, there are no circular rankings because say D>(A=B=C=E).

What is this ranking circularity called - Concordat blah blah???

Syd1435 11:48, 2004 Oct 16 (UTC)

Syd1435, please read the writeup on Instant Runoff Voting as well as the writeup on Condorcet method for an explanation of IRV's flaws, and a demonstration of why IRV has major tactical voting problems when a third party candidate reaches a level of popularity where it is possible that they could be elected. The point to take home here is that approval voting isn't perfect, but it is better than first past the post, and a good first step towards a true Condorcet method for elections. Instead of Instant Runoff Voting, perhaps you would approve of a ranked choice ballot, counted with Condorcet method? McCart42 20:49, 2005 Mar 9 (UTC)

Approval Voting can be converted into a form of Instant Runoff Voting by replacing YES with "1" and NO with "2"

• [2] Joe Smith ----- Greens.
• [1] Henry Ford ---- Rural Republican
• [2] Jane Doe ------ Democrat
• [2] Fred Rubble --- Reform
• [1] Mary Hill ----- City Republican

Note how the numbers "1" and "2" are repeated.

If a voter desires to preference Ford ahead of Hill, while supporting both these Republicans against all others, then that voter would need to use the numbers "1", "2" and "3".

This "1" = "FULL YES", "2" = "PART YES", "3" = "NO"

• [3] Joe Smith ----- Greens.
• [1] Henry Ford ---- Rural Republican
• [3] Jane Doe ------ Democrat
• [3] Fred Rubble --- Reform
• [2] Mary Hill ----- City Republican

It would not be Rocket Science to devise a (computerised) system to allow a voter to use either Approval Voting or Instant Runoff Voting in the same election.

• [3] Joe Smith ----- Greens.
• [1] Henry Ford ---- Rural Republican
• [4] Jane Doe ------ Democrat
• [5] Fred Rubble --- Reform
• [2] Mary Hill ----- City Republican

A convential Instant Runoff Voting requires each square to be filled in by different consequtive numbers, which helps the electoral officials check for errors.

Approval voting can be extended to multiple winner elections, either as block approval voting, a simple variant on block voting where each voter can select an unlimited number of candidates and the candidates with the most approval votes win, or as proportional approval voting which seeks to maximise the overall satisfaction with the final result using approval voting.

A disadvantage of multiple winner voting, is that if there are N vacancies, voters must vote for N candidates, which is like N First Past the Post votes in parallel. The result if often a clean sweep by one major party or the other.

Limited Voting allows each voter M votes for N vacancies, where M < N, which reduces the likely of a clean sweep.

Cumulative Voting allows each voter M votes for N vacancies, where M <= N, but the voter can allocate those votes 1 each for M candidates or M votes for just 1 candidate, or something in between.

AV is an abbreviation of "Alternate Vote aka IRV" as well as Approval Voting. Can something be done to disambiguate this, by say calling Approval Voting AppV?

Syd1435 10:56, 2004 Oct 16 (UTC)

The link to "The Science of Elections" requires a subscription. Is there a summary anywhere that can be viewed freely? --Townmouse 19:48, 16 Oct 2004 (UTC)

In contentious elections with a super-majority of voters who prefer their favorite candidate vastly over all others

Why do you want to use the term "super-majority" here? The old text said "full of." If you don't like that, then how about "many"? KVenzke 19:01, May 22, 2005 (UTC)

This post from the Election-methods mailing list in October 2004 is a response to the Center for Voting and Democracy's letter in support of instant-runoff voting over approval voting. It contains many good points on the nature of fairness in electoral methods. - McCart42 (talk) 04:11, 15 July 2005 (UTC)[reply]

I'm not too happy with how the Tenessee example is elaborated in the article page, in particular the sentence that ticks off the elaboration of that example:

Supposing that voters voted for their two favorite candidates, [...]

While that's typically not the kind of simplification approval voting makes.

I can understand a more complex example (than the new "simple example" I introduced) is needed to clarify how the "tactical" voting works, and other concepts related to approval voting that need explaining, I can even appreciate such "untypically simplified complex examples" come from handbooks written by serious people, but in the end I think it might be perfectly possible to lend & adapt an example (or set up one) that neither has the flaw of not being a real approval voting example, neither is too limited to explain the most important concepts relating to this type of voting.

For clarity: I have no problem whatsoever with Tennessee or whatever other state or country being used by way of example: only the example should not set the bad example (or even merely suggesting) of making the supposition that in an approval vote everyone votes for exactly two candidates.

I'd rewrite the example, but then I have no clue what even remotely likely data might have been for Tenessee; and also spilling these data in the article page might encumber the example with a degree of complexity not useful in explaining the base concepts.

Could anyone help out here?

--Francis Schonken 10:44, 25 August 2005 (UTC)[reply]

I don't agree with you that the Tennessee example is misleading. The only thing that could reasonably be done would be to consider also the cases that voters approve the top one or three candidates. A mixture of strategies wouldn't explain anything. KVenzke 04:34, September 12, 2005 (UTC)

User:Couvares added a bullet point: Approval voting is simple enough to carry out quickly in a live meeting without the aid of computers, complicated paperwork, or multiple rounds of voting. This makes it more practical than many other voting systems for small, democratic organizations such as labor unions.

I removed this opinion statement of "more practical" which ignores the difficulty for voters in quickly deciding how many candidates to support.

I'd actually be interested in separating two methods that fit under "approval":

1. Approval voting with a fixed number of winners.
2. Approval voting with fixed threshold for acceptance of a variable number of winners.

They are categorically different in voter strategy.

I consider Fixed-winner Approval Voting in live meetings a perfect example of how not to use approval.

I've seen it attempted. A dozen candidates were sequentially listed with people raising hands on each candidate for support. Voters couldn't easily keep track of the full list of candidates in their heads without anything written down. I believe candidates named near the end of the voting got less votes as people got saturated by choices. I believe other more careful voters (like myself) offered to few votes I was I unable to backup the voting and add my support for a previously announced candidate. It was a real mess.

On the other hand, a fixed-threshold approval vote might be used to select sequential discussion items:

For example, a progressive/efficient meeting chair might say "Brainstorming has produced 8 independent proposed soluions to our problem. To speed up discussion we'll in immediate sequence yes or no whether further discussion will be allowed for each proposal. Choices with 50% support will have 30 minutes of discussion following. Choices below 50% will be disregarded immediately."

Under a fixed-threshold system, undervoting on "fair choices" to help a favorite choice is discouraged for fear of losing ALL fair choices. Overvoting is discouraged only by the limits of patience of the voters to deal with more winners.

I could see something like this would seem "more democratic" than using simple "Robert's rules of order", with a single "motion" up at a time, and people being forced to vote on a final decision before knowing all the options.

I accept when the term "Approval Voting" is used, it is assumed to mean fixed-winner Approval.

I don't believe there is a practical use for "Approval voting" in live meetings because of the difficulties I offered above. A voting method shouldn't give more power to smarter people - people who can quickly apply strategy on how widely to vote.

Tom Ruen 04:45, 24 September 2005 (UTC)[reply]
UPDATED: Tom Ruen 07:12, 24 September 2005 (UTC)[reply]

The question was asked, where do they use approval voting?

The United Nations uses Approval Voting to select its Secretary-General; this highlights AV's ability to select the least objectionable candidate when voters vote their opinion (as opposed to "strategically voting").

Also, around 500 B.C., Athenians used annual disapproval voting to determine which politician they most wanted to exile (to prevent too many leaders from being banished, the rules were changed to require 6,000 such votes).

From: Fred Baldwin Ph.D, "Election Dissection - Different polls for different goals." July 2004. Attache http://www.attachemag.com/archives/07-04/features/story2.htm

Iarex 22:26, 30 November 2005 (UTC)iarex[reply]

Apparently the UN does NOT use multiple rounds of voting (from the link). I wonder if they care what "approval" level the winner gets? Do they care if one candidate gets 90% and another gets 89%? Do they care if no candidate gets 50%? Do they care if no candidate gets even 10%?

I still don't see any "live meetings" successfully using approval.

Tom Ruen 05:24, 24 September 2005 (UTC)[reply]

Tom, you seem to have a POV about whether Approval should be used in live meetings, which is not especially relevant to the article. I also see no reason to remove the fact that Approval is easy for live meetings; you can have the opinion that it's flawed, but that doesn't make it less easy.

Approval voting, as defined, has one round; if you have multiple rounds, then you're holding a runoff election that has much different properties. I have only ever witnessed one Approval runoff, and it was here on Wikipedia for the template standardization contest. (It went very badly.)

RSpeer 15:37, 24 September 2005 (UTC)[reply]

Given the fact that I have no evidence of Approval being used successfully in live meetings, my opinion would seem to be confirmed that Approval is not easy.

Tom Ruen 18:50, 24 September 2005 (UTC)[reply]

I had no problem with the voting procedure being described before using the singular they. The "he or she" strikes me as just a bit more awkward, but I don't think it's worth reverting over. rspeer / ɹəədsɹ 19:05, 24 December 2005 (UTC)[reply]

I removed the following "studies":

Thomas Colignatus (afaik his real name is Thomas Cool but he prefers Colignatus because he thinks it's cool) PDF: "The normal state in the world is “strategic voting” (cheating) and then AV collapses to “Plurality Voting” (PV), where people basically vote for their first candidate."

Emile C. J. Sheng PDF: "From a game theoretic standpoint, voters with ordinal preferences among the candidates are decreasing the influence of their ballots if they vote for multiple candidates; their votes are most decisive and influential when they concentrate their support on one candidate only."

Incorrect. Example: There are three candidates, A, B, C. A and B are well established. C is a complete newbie with almost no funding. I like C most, B almost as much and I despise A. If I am too proud to compromise so that I only vote for C, I give away the possibility to influence who wins. I will mark B. But making also a mark for C comes at 0 cost, so I will mark B AND C. --R.H. 01:22, 29 January 2006 (UTC)[reply]

• Those conclusions seem fairly dubious to me, yes, but the fact that you disagree with the studies is not a reason to remove them. Do you have a better reason? For example, have these papers not been peer reviewed and published? rspeer / ɹəədsɹ 07:44, 29 January 2006 (UTC)[reply]

Thomas Colignatus says that the status quo should have privileged status in voting systems. In general, giving no option a privilege is viewed as a feature (Neutrality Criterion) and not a bug . One can alter any method to have a status quo bias though.

See also my comment below. On this point here: there is a difference between technical and moral. Technically it is possible not to eat, but that does not mean that you should not eat. Technically you can present voting systems without the status quo given special position, and then it helps to see the features that arise; but morally you would want the pre-condition of the selection of points that are at least as good as the status quo, in order to protect minority rights. Thus, the term 'neutrality criterion' would be a technical phrase that can be misleading about its moral impact. Indeed, you can add tires to any car, but, it would be strange when car sales persons start selling cars without tires, since you can always add them yourself. Thus, voting theorists should think twice before presenting voting systems to the general public without the status quo pre-condition. Thus, I have always granted that 'technical neutrality' is a feature and that the status quo can be added, but my point was that from the angle of democratic theory, the issue is reversed. Thanks for referring to my work, but please refer accurately. Colignatus 22:59, 10 March 2006 (UTC)[reply]

Emile C. J. Sheng cites an example of voter preferences (I mean what is in their heads before they vote) outlined by Approval supporter Lin Jih-wen. It is the first scenario in the article. He claims Lin Jih-wen used this as an example how strategy-proof Approval is and then tries to use the same example to show the opposite. The scenario shows a Condorcet Cycle (he doesn't mention that it is one). What method doesn't look bad with a genuine Condorcet Cycle? (IRV for example fails Reversal Symmetry in such situations). Given that genuine Condorcet Cycles happen rather seldom (according to simulations posted on the electorama mailing list those occur with non-strategizing voters with a likeliness of 5%-10%) it probably doesn't tell much positive or negative about Approval.

He proceeds to describe how in that situation voters have to vote somebody over their true favorite to prevent the one they dislike most from winning. "How is that possible?" you might ask, given that according to Mike Ossipoff and others there is no reason to put somebody above your favourite (Favorite Betrayal Criterion). Well, the Condorcet Cycle is not enough for that, you must also change the votes from being cast at the same time with protecting privacy.

I don't think Brams advocates that.

He continues by saying Approval fails the "monotonicity condition". The wikipedia article says it passes. Douglas Woodall has several criteria that he calls mono-something and he calls what is normally called monotonicity "mono-raise". What Sheng means by "monotonicity condition" he never says. --R.H. 19:09, 29 January 2006 (UTC)[reply]

I wonder whether non-preferential Approval voting (cf. Preferential voting) has to be (game theory) or usually is against the representation of minorities. Taking an example from e.g. staff representations or union elections: 3000 possible votes, 11 choices on ballot, 7 of those 11 will get a seat, a minority of 500 (17%) which is 100% for representation of 1 person, usually get's not represented.

My question: is this mathematically inevitable?

• Is it worse the more unpreferred choices there are on the ballot paper?
• If this problem is known, how to improve it?
• How to improve it in an acceptable way for the majority - otherwise you don't get it done.

If this problem is already addressed here somewhere, please point to it.

Are the voting simulating programs, where one could test things and experiment with voting behaviour of groups of voters? Tommie 12:26, 30 January 2006 (UTC)[reply]

Approval Voting in general means the single winner method described in the article. Multiwinner doesn't necessarily mean proportional.

The first winner with Block voting is probably a great centrist (especially if you are allowed to make as many marks as you want), the second winner makes an almost as good centrist, the third winner is almost as good at being a centrist as the second etc. The reason why simply taking the top vote getters as winners is unlikely to produce proportional results is because Approval Voting is a good method to elect a centrist. This also tells us something about single mark ballots. The reason why lone mark plurality ballots can be used for more proportional representation or runoffs with exciting debates among interestingly different candidates is because lone mark is so bad at electing centrists.

Here is a worst case scenario with block voting: Suppose there is a strong divide with people divided into camps so that everybody in a camp votes for every candidate from that same camp and nobody else. Group A is 20% of the voters, group B 19%, group C 18%, group D 17%, group E 16%, group F 10%. 10 seats to get. If 2 candidatas from group A run, they both get a seat which is fine. If 3 candidates from group A run, they all get a seat. Well, it is very seldom possible to give seats exactly according to the votes, there are basically always rounding errors. But what if 4 candidates from that group run, or 5, or even 10? They will all get a seat.

Marking a candidate that doesn't get a seat shouldn't cost the voter something (like it does with cumulative voting). But a ballot that is successful at electing a candidate for the first seat must be downgraded in voting power for the next round of counting so that voters who got shafted in the first round have more say in the second round which picks the second winner. This is what the method by Thorvald Thiele does. It is described at the end of the Proportional approval voting article (the nonsequential version described before that gives more proportional results but needs a computer). The method by Thiele has been criticized because the amount of downgrading a ballot gets is only determined by how often it is successful at electing a candidate. Suppose there is a highly divided electorate and the first seat goes to somebody only approved on 10% of the ballots. Each of those ballots get downgraded to one half in the second round. Compare that to an electorate that strongly supports one candidate so the first seat goes to somebody approved on 90% of the ballots. According to Thiele each of those ballots get downgraded to one half for the second round as well. E. Phragmén developed a counting method that recognizes the difference: Olli Salmi on (Sequential) PAV and Phragmén --R.H. 15:16, 30 January 2006 (UTC)[reply]

I just entered a User talk page http://en.wikipedia.org/wiki/User_talk:Colignatus and, to check that it had been entered correctly, I did a search and also noted this page. Two Points: (1) It appears that there had been a link to a paper of mine, that R.H. however removed again. It appears that I have been quoted correctly that AV "basically" comes down to PV. But R.H. neglects this "basically" and gives an example where there is a small difference. My point however was that, granted that such exceptions exist, the rule is that AV ~ PV. I emphasize this point since my research shows that a Borda Fixed Point approach would be best, considering common conditions, so that all research into AV most likely is a dead end. (2) One question was whether my paper on AV has been peer-reviewed. No, my papers generally aren't, since I wait till the censorship of science by the Dutch government has been solved, and then I can start joining the usual scientific process again. In the mean time I put my work on the web so that people can see what the censorship is about. (1) + (2) I would enjoy if the reference is restored, though will not do so myself, not only for the above, but in particular since the issue of the Status Quo is important in that paper as will, which issues tends to be overlooked in voting theory ("tends" is not "is"). Thanks for the good work. Colignatus 21:38, 27 February 2006 (UTC)[reply]

I've come across an interesting discussion of the possibility of an approval-disapproval voting system. Take this example:

[DISCLAIMER: I'm not a Libertarian or pushing an agenda.]

I'm a Libertarian voter - for both free market and what I view as civil rights. My choices are as follows:

Libertarian Party - Share nearly all values.
Democratic Party - Share some social and economic values.
Republican Party - Share few social values and many economic values.
Green Party - Share many social values and few economic values.
Constitution Party - Share few social values and some economic values.
Socialist Party - Share some social values and few economic values.

I obviously prefer the Libertarian Party over everyone else, but I also obviously would very much not want to see a Socialist or Constitutionalist win. Depending on whether I value social or economic values higher, I might prefer either the Greens or the Republicans, or I may compromise and choose the Democrats. However, any would be solid choices over the Socialists and Constitutionalists. Therefore, I might want to vote thus:

[FOR] - Libertarian
[NEUTRAL] - Democratic
[NEUTRAL] - Republican
[NEUTRAL] - Green
[AGAINST] - Constitution
[AGAINST] - Socialist

Then, my vote might be counted as +1 for the Libertarian Party and -1 each for the Constitution and Socialist Parties. Extrapolate this across an electorate of 25,000 and you might get something resembling the following:

Libertarian: 10,000 FOR/11,000 NEUTRAL/4,000 AGAINST = 6,000
Democratic: 12,000 FOR/6,000 NEUTRAL/7,000 AGAINST = 5,000
Republican: 13,000 FOR/3,000 NEUTRAL/9,000 AGAINST = 4,000
Green: 11,000 FOR/5,000 NEUTRAL/9,000 AGAINST = 2,000
Constitution: 5,000 FOR/13,000 NEUTRAL/7,000 AGAINST = -2,000
Socialist: 6,000 FOR/10,000 NEUTRAL/9,000 AGAINST = -3,000

In which the Libertarian candidate, who has the greatest majority of approval votes over disapproval votes, wins the election.

Since I think this method has some level of support, I wonder if it should be included in the article. Cheers! —Cuiviénen, Sunday, 19 March 2006 @ 19:16 (UTC)