[Koha] Koha license upgrade voting method
Clay Shentrup
clay at electology.org
Sun Feb 6 10:52:03 NZDT 2011
Woaaahhhhhh buddy, gimme some time to get to this little tome. :)
On Wed, Feb 2, 2011 at 2:01 AM, Thomas Dukleth <kohalist at agogme.com> wrote:
> Reply inline:
>
>
> On Tue, January 18, 2011 05:33, Clay Shentrup wrote:
> > On Fri, Jan 14, 2011 at 10:14, Thomas Dukleth <kohalist at agogme.com>
> wrote:
>
> [...]
>
> >> In another message, I will address the important issues of voting
> strategy
> >> with score voting.
> >>
> > Discussions of "strategy" are frequently plagued with logical fallacies,
> > and
> > a lack of awareness of key concepts like Bayesian regret. Here are some
> > links which help to inform on this complex and counterintuitive issue.
> >
> > http://www.electology.org/tactical-voting
> > http://www.electology.org/bullet-voting
> > http://scorevoting.net/UniqBest.html
> > http://scorevoting.net/StratHonMix.html
> > http://scorevoting.net/PleasantSurprise.html
> > http://scorevoting.net/AppCW.html
> > http://www.electology.org/threshold
> > http://scorevoting.net/RVstrat3.html
> > http://scorevoting.net/RVstrat4.html
>
> I had read these and much more before I had proposed to present a message
> about strategy. However, even prior to reading much about score voting I
> had independently and intuitively taken much of the same conclusions about
> strategy. Finding strategies intuitively does not mean that I am immune
> from falling for some fallacies.
>
> Optimal score voting strategy may be intuitive to many people but does
> introduce a complexity to voting for which people are unaccustomed and
> raises the dilemma between honest voting and strategic voting.
>
> [...]
>
> >> [In a later message, I will propose a means
> >> for
> >> resolving some issues of voting strategy.]
> >>
> >
> > I will bet you a year's salary that your ideas here have been discussed
> to
> > death on our Yahoo discussion group a myriad of times over the past 5
> > years.
> > :)
>
> I doubt that any of the following summary of strategy is original.
>
> People may have already proposed all logical variants to resolve issues of
> strategic complexity and the honest vs. strategic dilemma. There is a
> chance the scheme which I will present in another message for resolution
> may be an original contribution to voting theory specifically developed to
> solve the problem of finding a good voting method for the Koha community.
>
> [...]
>
> Difficulties of voting strategy are the most significant weakness of score
> voting (range voting) and need to be understood by the electorate and even
> better constrained by limitations to avoid mimicing the problems of voting
> methods which often fail to maximise voter preferences.
>
> Revoting to consensus may be helpful for some problems of voting strategy
> with score voting. Unfortunately, rational strategic voting undermines
> the informative value of honestly reported assignment of scores without
> applying strategy. Honestly reported information can be especially
> informative for discussing how to achieve consensus.
>
> The following consideration of voting strategy for score voting is lengthy
> and I suspect may be considered excessively tedious. Most people may
> think that voting should be simpler and that voting should not need an
> understanding of voting strategy. I agree that voting should be simple
> but also avoid the worst problems of plurality voting familiar to us all
> in which candidates which most voters oppose often win. Merely
> understanding that voting strategy can have an effect on which candidate
> wins may be sufficient for most people.
>
> The scheme which I will present in another message eliminates the problem
> of voting strategy complexity with score voting in addition to resolving
> the dilemma between honest and strategic voting.
>
>
> 1. NOMENCLATURE.
>
> 1.1. HONEST VOTING AND STRATEGIC VOTING.
>
> The literature has possibly confusing references to 'honest voting' as
> distinct from 'strategic voting'.
>
> 'Honest voting' (sincere voting) is merely an individual voter directly
> expressing the voter's internal preferences without considering how to
> best express them in a manner most likely to win in relation to votes cast
> by other voters. 'Honest voting' might be described as naive voting by
> not considering chances of the voter's prefered candidates winning.
>
> 'Strategic voting' is voting with an understanding of how an individual
> voter can maximise his preferences for candidates in the context of votes
> by other voters. 'Strategic voting' would only be dishonest if the
> rational strategy for some election scenario encouraged casting some votes
> contrary to actual preferences to give the voter's greatest preference the
> best chance of winning. Fortunately, score voting is least likely voting
> method to involve scenarios in which voting contrary to actual preferences
> might be a successful strategy for an individual voter.
>
> The distinction between 'honest voting' and 'strategic voting' may be
> confusing if one assumes that the goal of each individual voter is to have
> his own greatest preference win. Given the goal of winning, strategic
> voting is merely rational and should not be considered somehow dishonest.
> It would be irrational for individual voters to ignore the other voters
> and for individual voters to thus not attempt to have their own preference
> win.
>
>
> 1.2. APPROVAL AND RANKING IN SCORE VOTING.
>
> 'Approval voting' is simple yes or no voting for each candidate.
> 'Approval voting' is a type of score voting in which the range of
> permitted scores is limited to two values such as either 0 or 1.
>
> 'Ranking' is used to list relative preferences between candidates in order
> for 'preference voting methods'. 'Score voting' uses scores for
> expressing absolute preferences for candidates not merely relative
> preferences between candidates.
>
> 'Ranked approval voting' is a somewhat contradictory name which I have
> given for part of a voting strategy in which votes are expressed as
> adjacent scores clustered adjacent to either the highest or lowest scores
> in the permitted range. The clustering has elements of both 'approval
> voting' and 'preference voting methods'. Examples are given further below
> in the context of possible strategies.
>
>
> 2. STATEGICALLY POOR VOTING STRATEGIES.
>
> Strategically poor voting strategies can easily be avoided when
> recognised. However, some forms of 'honest voting' may also be
> strategically poor voting which is a problem which needs correcting in the
> voting method.
>
>
> 2.1. WEAK VOTING.
>
> Weak voting is applying something less than the highest scores in the
> possible range for the voter's greatest prefered candidates and something
> more than the lowest permitted scores in the range for the voter's least
> preferred candidates. Weak voting might be an honest expression of
> similarities between candidates but a poor strategy for maximising
> individual preferences in the cumulative result of all voters. Other
> voters using strong voting, applying the highest possible scores in the
> range for greatly prefered candidates and the lowest possible scores in
> the range for least prefered candidates, would outvote weak voters.
>
>
> 2.1.1. EXAMPLES OF WEAK VOTING.
>
> 2.1.1.1. WEAK VOTING EXAMPLE.
>
> Score range allows scores from 0 to 10.
> Candidates are A, B, C, and D.
> 300 people vote.
>
> 200 voters score candidates weakly:
> A at 7, B at 6, C at 5, and D at 4.
>
> 100 voters score candidates strongly with opposite preference ranking to
> other voters:
> A at 0, B at 1, C at 9, and D at 10.
>
> Calculating the averages:
>
> Candidate A:
> ((7 score * 200 votes) +
> (0 score * 100 votes)) /
> 300 total votes =
> 4.6667 average mean score
>
> Candidate B:
> ((6 score * 200 votes) +
> (1 score * 100 votes)) /
> 300 total votes =
> 4.3333 average mean score
>
> Candidate C:
> ((5 score * 200 votes) +
> (9 score * 100 votes)) /
> 300 total votes =
> 6.3333 average mean score
>
> Candidate D:
> ((4 score * 200 votes) +
> (10 score * 100 votes)) /
> 300 total votes =
> 6 average mean score
>
> Candidates C won. Voters who had used weak scores had some effect on the
> outcome in enabling C to beat D. However, voters who had used weak scores
> could have enabled their greatest preferred candidate A to win if they had
> used strong scores.
>
>
> 2.1.1.2. PARTLY CORRECTED WEAK VOTING EXAMPLE.
>
> Weak voting can be at least partly corrected by simply using the highest
> and lowest scores permissible in the range.
>
> Score range allows scores from 0 to 10.
> Candidates are A, B, C, and D.
> 300 people vote.
>
> 200 voters score candidates with corrections to use the highest and lowest
> scores:
> A at 10, B at 6, C at 5, and D at 0.
>
> 100 voters score candidates strongly with opposite preference ranking to
> the other voters:
> A at 0, B at 1, C at 9, and D at 10.
>
> Calculating the averages:
>
> Candidate A:
> ((10 score * 200 votes) +
> (0 score * 100 votes)) /
> 300 total votes =
> 6.6667 average mean score
>
> Candidate B:
> ((6 score * 200 votes) +
> (1 score * 100 votes)) /
> 300 total votes =
> 4.3333 average mean score
>
> Candidate C:
> ((5 score * 200 votes) +
> (9 score * 100 votes)) /
> 300 total votes =
> 6.3333 average mean score
>
> Candidate D:
> ((0 score * 200 votes) +
> (10 score * 100 votes)) /
> 300 total votes =
> 3.3333 average mean score
>
> Candidate A won. Correcting weak voting by using the highest and lowest
> scores permissible in the range allowed the majority preference for
> candidate A to win.
>
>
> 2.2. BULLET VOTING.
>
> Plurality voting could be used as a strategy. If many voters would use
> plurality voting as strategy, then a plurality result would be the
> unfortunate consequence in the absence of an absolute majority.
>
> Plurality voting as a strategy instead of a voting method is bullet voting.
>
> Voters might assign the highest possible score to their greatest prefered
> candidate and the lowest possible score to all other candidates. Such a
> voting pattern would reduce score voting to common bad plurality voting in
> which the candidate with most votes can win despite being opposed by the
> majority of voters.
>
>
> 2.2.1. EXAMPLES OF BULLET VOTING.
>
> 2.2.1.1. BULLET VOTING EXAMPLE.
>
> Score range allows scores from 0 to 10.
> Candidates are A, B, C, and D.
> 300 people vote.
>
> 98 voters score candidates:
> A at 10, B at 0, C at 0, and D at 0.
>
> 97 voters score candidates:
> A at 0, B at 10, C at 0, and D at 0.
>
> 97 voters score candidates:
> A at 0, B at 0, C at 10, and D at 0.
>
> 8 voters score candidates:
> A at 0, B at 0, C at 0, and D at 10.
>
> Calculating the averages:
>
> Candidate A:
> ((10 score * 98 votes) +
> (0 score * 202 votes)) /
> 300 total votes =
> 3.2667 average mean score
>
> Candidate B:
> ((10 score * 97 votes) +
> (0 score * 203 votes)) /
> 300 total votes =
> 3.2333 average mean score
>
> Candidate C:
> ((10 score * 97 votes) +
> (0 score * 203 votes)) /
> 300 total votes =
> 3.2333 average mean score
>
> Candidate D:
> ((10 score * 8 votes) +
> (0 score * 292 votes)) /
> 300 total votes =
> 0.2667 average mean score
>
> Candidate A won for having the highest average mean score despite being
> opposed by the majority of voters merely because of a poor strategy to
> express only the greatest preference.
>
> Computer simulations by Warren Smith show that plurality voting is the
> best strategy for an individual voter if there are a small number of
> voters, http://www.scorevoting.net/RVstrat3.html . In simulations of a
> three candidate election, plurality voting was found the best strategy for
> an individual voter if there are not more than ten voters.
>
> A plurality vote without an absolute majority should be avoided by a rule
> that the problem will either be corrected by revoting or the automatic
> substitution of required preference ranking.
>
>
> 2.2.1.2. PREFERENCE RANKING REQUIREMENT WITH BULLET VOTING EXAMPLE.
>
> Score range allows scores from 0 to 10.
> Candidates are A, B, C, and D.
> 300 people vote.
>
> Minimal preference ranks are required for scores preventing multiple 0
> scores.
>
> 98 voters score candidates:
> A at 10, B at 2, C at 1, and D at 0.
>
> 97 voters score candidates:
> A at 0, B at 10, C at 2, and D at 1.
>
> 97 voters score candidates:
> A at 1, B at 0, C at 10, and D at 2.
>
> 8 voters score candidates:
> A at 2, B at 1, C at 0, and D at 10.
>
> Calculating the averages:
>
> Candidate A:
> ((10 score * 98 votes) +
> (0 score * 97 votes) +
> (1 score * 97 votes) +
> (2 score * 8 votes)) /
> 300 total votes =
> 3.6433 average mean score
>
> Candidate B:
> ((2 score * 98 votes) +
> (10 score * 97 votes) +
> (0 score * 97 votes) +
> (1 score * 8 votes)) /
> 300 total votes =
> 3.9133 average mean score
>
> Candidate C:
> ((1 score * 98 votes) +
> (2 score * 97 votes) +
> (10 score * 97 votes) +
> (0 score * 8 votes)) /
> 300 total votes =
> 4.2067 average mean score
>
> Candidate D:
> ((0 score * 98 votes) +
> (1 score * 97 votes) +
> (2 score * 97 votes) +
> (10 score * 8 votes)) /
> 300 total votes =
> 1.2367 average mean score
>
> Candidate C won. Required preference ordering prevented candidate A for
> having the highest average mean score despite being opposed by the
> majority of voters merely because of a poor strategy to express only the
> greatest preference.
>
>
> 3. OPTIMISED VOTING.
>
> In optimised voting, a voter applies the highest possible score in the
> range for the greatest prefered candidate and the lowest possible score in
> the range for the least prefered candidate. The difficulty is what to do
> about the candidates which are neither the greatest preference nor the
> least preference.
>
> If a voter assigns too high a score to one of the voter's middle
> preference candidates, then the high score may help defeat a candidate for
> which the voter has a greater preference. If a voter assigns too low a
> score to one of the voter's middle preference candidates, then the voter
> may help the candidate loose to a candidate for which the voter has a
> lesser preference.
>
>
> 3.1. SCALED SINCERITY.
>
> Scaled sincerity voting assigns middle preference candidate scores by
> evenly distribution (linear interpolation) across the range of permissible
> scores.
>
> Such an even distribution of scores for candidates would be similar to a
> Borda count in which weights (scores) are assigned according to relative
> preference rank. The most significant difference is that Borda would not
> have a weight of 0 for the lowest ranking preference.
>
> No analysis of middle preferences except relative ranking by the voter is
> needed for scaled sincerity, therefore, the strategy can be used in
> circumstances when no other strategy may be determined. In simulations of
> millions of election scenarios, scaled sincerity performed at least 91% as
> well as the optimum strategy, http://www.scorevoting.net/RVstrat3.html .
>
> 3.1.1. EXAMPLE OF SCALED SINCERITY.
>
> Example of scaled sincerity.
>
> Score range allows scores from 0 to 10.
> Candidates are A, B, C, and D.
>
> The voter has relative preferences A > B > C > D. Scores for the
> preferences are evenly distributed as well as can be managed within the
> range:
> A at 10, B at 7, C at 3, and D at 0.
>
>
> 3.2. MEAN BASED THRESHOLDING.
>
> 3.2.1. MEAN BASED THRESHOLDING GENERALLY.
>
> Mean based thresholding strategy uses the expected utility of the result
> for the voter to determine a threshold as a dividing point for optimising
> scores either high or low. See the expected utility hypothesis in
> Wikipedia, http://en.wikipedia.org/wiki/Expected_utility_hypothesis . The
> expected utility may be adjusted by a risk avoidance bias which would
> change the threshold. The mean threshold may be adjusted by combining the
> expected utility with some expectation or actual knowledge of how other
> voters may vote.
>
> Expected utility of the result can be calculated by the voter first
> considering honest scores for middle preference candidates and then
> calculating the average mean for the scores assigned for all the
> candidates.
>
> The voter assigns the highest permitted scores to candidates with a first
> considered honest score above the calculated threshold and the lowest
> permitted scores to candidates equal to or below the threshold.
>
> Such a mean based thresholding strategy was found to be the most
> successful strategy in simulations of millions of elections,
> http://www.scorevoting.net/RVstrat3.html .
>
>
> 3.2.1.1. EXAMPLE OF MEAN BASED THRESHOLDING.
>
> Score range allows scores from 0 to 10.
> Candidates are A, B, C, and D.
>
> In considering honest scores which might be assigned in the absence of
> strategy, a voter has the following preferences indicating the voter's
> expected utility for each of the candidates:
> A at 10, B at 6, C at 2, and D at 0.
>
> Calculating mean threshold of expected utility:
> ((10 score * 1 candidate) +
> (6 score * 1 candidate) +
> (2 score * 1 candidate) +
> (0 score * 1 candidate)) /
> 4 candidates =
> 4.5 mean threshold
>
> The voter assigns the highest scores in the permitted range to candidates
> with an expected utility above the mean threshold of 4.5. The voter
> assigns the lowest scores in the permitted range to candidates with an
> expected utility equal to or below the mean threshold of 4.5.
>
> Approval form with only highest and lowest scores:
> A at 10, B at 10, C at 0, and D at 0.
>
> Ranked approval form with scores adjacent to highest and lowest:
> A at 10, B at 9, C at 1, and D at 0.
>
>
> 3.2.2. RISK AVOIDANCE BIAS.
>
> The expected utility may be adjusted by considering a greater voter bias
> over risk avoidance. When the risk avoidance bias is sufficiently great,
> the risk avoidance has a decisive effect on expected utility of some
> candidates and consequently the position of the threshold dividing between
> optimising scores high or low.
>
> Ordinarily one of the great advantages of score voting is that scores can
> have a degree of candidate independent absolute value. Adding or
> subtracting candidates need not have any effect on how a voter asses
> individual candidates, in contrast to preference voting in which
> assessments are all relative to other candidates. However, the permitted
> range needs to be sufficiently large to account for meaningful differences
> between candidates.
>
> Candidates may exist for which a voter has an indispensably high utility
> that alternatives must be avoided or such a horribly low utility that the
> horrible candidates must be avoided. At either the high or low end of the
> range, the permitted range may be insufficient to include such cases and
> have the scale meaningfully differentiate candidates. Scores considered
> for candidates should have some sense of relative expected utility in
> relation to other candidates.
>
> For example, the permitted range for scores of 0 to 10 is useful for a
> voter to consider the expected utility of candidates A at 10, B at 6, and
> C at 0. However, candidate D may be indispensably valuable and may have
> an expected utility of 1,000 which is outside the permitted range.
> Alternatively, candidate D may have a horribly low value to be avoided
> that the candidate may have an expected value of -1000. Incorporating
> indispensable D at the top of the range with score 10 should squash the
> scale for the other candidates to scores near 0. Alternatively,
> incorporating horrible D at bottom of the range with score 0 should squash
> the scale for the other candidates to scores near 10.
>
> Distance between extreme alternatives within the permitted range should be
> maximised for risk avoidance. If some candidates are indispensable, they
> should have the highest permitted scores and all other candidates should
> have the lowest permitted scores to avoid the others. If some candidates
> are indispensable, they should have the highest permitted scores and all
> other candidates should have the lowest permitted scores to avoid the
> others.
>
> If there is only one indispensable candidate or only one horrible
> candidate for the voter, then the optimal voting strategy becomes a form
> of bullet (plurality) voting as described further above in section 2.2.
> In such a circumstance, bullet voting would not be a poor strategy as
> described above, but the optimal strategy for the voter.
>
>
> 3.2.2.1. EXAMPLES OF RISK AVOIDANCE.
>
> [Unlike other cases, 5 candidates may better show what happens to
> individual candidates.]
>
>
> 3.2.2.1.1. INDISPENSABLE CANDIDATES RISK AVOIDANCE EXAMPLE.
>
> Score range allows scores from 0 to 10.
> Candidates are A, B, C, D, and E.
>
> Either candidate A or B are indispensable to the voter with A preferred to
> B.
>
> In considering honest scores which might be assigned in the absence of
> strategy and ignoring the range restriction, a voter has the following
> preferences indicating the voter's expected utility for each of the
> candidates:
> A at 1000, B at 700, C at 10, D at 6, and E at 0.
>
> Calculating mean threshold of expected utility:
> ((1000 score * 1 candidate) +
> (700 score * 1 candidate) +
> (10 score * 1 candidate) +
> (6 score * 1 candidate) +
> (0 score * 1 candidate)) /
> 5 candidates =
> 343.2 mean threshold
>
> The voter assigns the highest scores in the permitted range to candidates
> with an expected utility above the mean threshold of 343.2. The voter
> assigns the lowest scores in the permitted range to candidates with an
> expected utility equal to or below the mean threshold of 343.2.
>
> Approval form with only highest and lowest scores:
> A at 10, B at 10, C at 0, D at 0, and E at 0.
>
> Ranked approval form with scores adjacent to highest and lowest:
> A at 10, B at 9, C at 2, D at 1, and E at 0.
>
>
> 3.2.2.1.2. HORRIBLE CANDIDATES RISK AVOIDANCE EXAMPLE.
>
> Score range allows scores from 0 to 10.
> Candidates are A, B, C, D, and E.
>
> Candidates D and E are both horrible to the voter with D preferred to E.
>
> In considering honest scores which might be assigned in the absence of
> strategy and ignoring the range restriction, a voter has the following
> preferences indicating the voter's expected utility for each of the
> candidates:
> A at 10, B at 6, C at 0, D at -700, and E at -1000.
>
> Calculating mean threshold of expected utility:
> ((10 score * 1 candidate) +
> (6 score * 1 candidate) +
> (0 score * 1 candidate) +
> (-700 score * 1 candidate) +
> (-1000 score * 1 candidate)) /
> 5 candidates =
> -336.8 mean threshold
>
> The voter assigns the highest scores in the permitted range to candidates
> with an expected utility above the mean threshold of -336.8. The voter
> assigns the lowest scores in the permitted range to candidates with an
> expected utility equal to or below the mean threshold of -336.8.
>
> Approval form with only highest and lowest scores:
> A at 10, B at 10, C at 10, D at 0, and E at 0.
>
> Ranked approval form with scores adjacent to highest and lowest:
> A at 10, B at 9, C at 8, D at 1, and E at 0.
>
>
> 3.2.2.1.3. INDISPENSABLE AND HORRIBLE CANDIDATES RISK AVOIDANCE EXAMPLE.
>
> Score range allows scores from 0 to 10.
> Candidates are A, B, C, D, and E.
>
> Candidate A is indispensable to the voter with A preferred to B.
> Candidates D and E are both horrible to the voter with D preferred to E.
>
> In considering honest scores which might be assigned in the absence of
> strategy and ignoring the range restriction, a voter has the following
> preferences indicating the voter's expected utility for each of the
> candidates:
> A at 1000, B at 6, C at 0, D at -700, and E at -1000.
>
> Adjusting the scale for the expected utilities to a scale of non-negative
> integers:
> A at 2000, B at 1006, C at 1000, D at 300, and E at 0.
>
> Calculating mean threshold of expected utility:
> ((1000 score * 1 candidate) +
> (6 score * 1 candidate) +
> (0 score * 1 candidate) +
> (-700 score * 1 candidate) +
> (-1000 score * 1 candidate)) /
> 5 candidates =
> -138.8 mean threshold
>
> The voter assigns the highest scores in the permitted range to candidates
> with an expected utility above the mean threshold of -138.8. The voter
> assigns the lowest scores in the permitted range to candidates with an
> expected utility equal to or below the mean threshold of -138.8.
>
> Approval form with only highest and lowest scores:
> A at 10, B at 10, C at 10, D at 0, and E at 0.
>
> Ranked approval form with scores adjacent to highest and lowest:
> A at 10, B at 9, C at 8, D at 1, and E at 0.
>
>
> 3.2.3. THRESHOLD ADJUSTMENT.
>
> 3.2.3.1. EXPECTATION OF OTHER VOTERS' PATTERNS.
>
> If an expectation of the candidate scoring patterns for other voters is
> known, then that expectation can be incorporated into the threshold
> calculation. See the threshold strategy as described by Clay Shentrup's
> organisation, The Center for Election Science,
> http://www.electology.org/threshold .
>
>
> 3.2.3.2. KNOWLEDGE OF OTHER VOTERS' PATTERNS.
>
> If there is actual knowledge of how other voters have already scored
> candidates in an ongoing election, then that knowledge can be incorporated
> into the threshold calculation. We should have knowledge of how other
> voters have already scored candidates during the voting period for
> revoting to consensus. However, consensus discussion should help everyone
> optimise votes more than a simple threshold calculation for individual
> voters.
>
>
> Thomas Dukleth
> Agogme
> 109 E 9th Street, 3D
> New York, NY 10003
> USA
> http://www.agogme.com
> +1 212-674-3783
>
>
>
--
*Clay Shentrup*
*Secretary, Director*
*The Center for Election Science*
*http://www.electology.org/*
*206.801.0484*
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