[Koha] Koha license upgrade voting method

[Thomas Dukleth]

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