Woaaahhhhhh buddy, gimme some time to get to this little tome. :)<br><br><div class="gmail_quote">On Wed, Feb 2, 2011 at 2:01 AM, Thomas Dukleth <span dir="ltr"><<a href="mailto:kohalist@agogme.com">kohalist@agogme.com</a>></span> wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;"><div class="im">Reply inline:<br>
<br>
<br>
On Tue, January 18, 2011 05:33, Clay Shentrup wrote:<br>
</div><div class="im">> On Fri, Jan 14, 2011 at 10:14, Thomas Dukleth <<a href="mailto:kohalist@agogme.com">kohalist@agogme.com</a>> wrote:<br>
<br>
</div>[...]<br>
<div class="im"><br>
>> In another message, I will address the important issues of voting strategy<br>
>> with score voting.<br>
>><br>
> Discussions of "strategy" are frequently plagued with logical fallacies,<br>
> and<br>
> a lack of awareness of key concepts like Bayesian regret. Here are some<br>
> links which help to inform on this complex and counterintuitive issue.<br>
><br>
> <a href="http://www.electology.org/tactical-voting" target="_blank">http://www.electology.org/tactical-voting</a><br>
> <a href="http://www.electology.org/bullet-voting" target="_blank">http://www.electology.org/bullet-voting</a><br>
> <a href="http://scorevoting.net/UniqBest.html" target="_blank">http://scorevoting.net/UniqBest.html</a><br>
> <a href="http://scorevoting.net/StratHonMix.html" target="_blank">http://scorevoting.net/StratHonMix.html</a><br>
> <a href="http://scorevoting.net/PleasantSurprise.html" target="_blank">http://scorevoting.net/PleasantSurprise.html</a><br>
> <a href="http://scorevoting.net/AppCW.html" target="_blank">http://scorevoting.net/AppCW.html</a><br>
> <a href="http://www.electology.org/threshold" target="_blank">http://www.electology.org/threshold</a><br>
> <a href="http://scorevoting.net/RVstrat3.html" target="_blank">http://scorevoting.net/RVstrat3.html</a><br>
> <a href="http://scorevoting.net/RVstrat4.html" target="_blank">http://scorevoting.net/RVstrat4.html</a><br>
<br>
</div>I had read these and much more before I had proposed to present a message<br>
about strategy. However, even prior to reading much about score voting I<br>
had independently and intuitively taken much of the same conclusions about<br>
strategy. Finding strategies intuitively does not mean that I am immune<br>
from falling for some fallacies.<br>
<br>
Optimal score voting strategy may be intuitive to many people but does<br>
introduce a complexity to voting for which people are unaccustomed and<br>
raises the dilemma between honest voting and strategic voting.<br>
<br>
[...]<br>
<div class="im"><br>
>> [In a later message, I will propose a means<br>
>> for<br>
>> resolving some issues of voting strategy.]<br>
>><br>
><br>
> I will bet you a year's salary that your ideas here have been discussed to<br>
> death on our Yahoo discussion group a myriad of times over the past 5<br>
> years.<br>
> :)<br>
<br>
</div>I doubt that any of the following summary of strategy is original.<br>
<br>
People may have already proposed all logical variants to resolve issues of<br>
strategic complexity and the honest vs. strategic dilemma. There is a<br>
chance the scheme which I will present in another message for resolution<br>
may be an original contribution to voting theory specifically developed to<br>
solve the problem of finding a good voting method for the Koha community.<br>
<br>
[...]<br>
<br>
Difficulties of voting strategy are the most significant weakness of score<br>
voting (range voting) and need to be understood by the electorate and even<br>
better constrained by limitations to avoid mimicing the problems of voting<br>
methods which often fail to maximise voter preferences.<br>
<br>
Revoting to consensus may be helpful for some problems of voting strategy<br>
with score voting. Unfortunately, rational strategic voting undermines<br>
the informative value of honestly reported assignment of scores without<br>
applying strategy. Honestly reported information can be especially<br>
informative for discussing how to achieve consensus.<br>
<br>
The following consideration of voting strategy for score voting is lengthy<br>
and I suspect may be considered excessively tedious. Most people may<br>
think that voting should be simpler and that voting should not need an<br>
understanding of voting strategy. I agree that voting should be simple<br>
but also avoid the worst problems of plurality voting familiar to us all<br>
in which candidates which most voters oppose often win. Merely<br>
understanding that voting strategy can have an effect on which candidate<br>
wins may be sufficient for most people.<br>
<br>
The scheme which I will present in another message eliminates the problem<br>
of voting strategy complexity with score voting in addition to resolving<br>
the dilemma between honest and strategic voting.<br>
<br>
<br>
1. NOMENCLATURE.<br>
<br>
1.1. HONEST VOTING AND STRATEGIC VOTING.<br>
<br>
The literature has possibly confusing references to 'honest voting' as<br>
distinct from 'strategic voting'.<br>
<br>
'Honest voting' (sincere voting) is merely an individual voter directly<br>
expressing the voter's internal preferences without considering how to<br>
best express them in a manner most likely to win in relation to votes cast<br>
by other voters. 'Honest voting' might be described as naive voting by<br>
not considering chances of the voter's prefered candidates winning.<br>
<br>
'Strategic voting' is voting with an understanding of how an individual<br>
voter can maximise his preferences for candidates in the context of votes<br>
by other voters. 'Strategic voting' would only be dishonest if the<br>
rational strategy for some election scenario encouraged casting some votes<br>
contrary to actual preferences to give the voter's greatest preference the<br>
best chance of winning. Fortunately, score voting is least likely voting<br>
method to involve scenarios in which voting contrary to actual preferences<br>
might be a successful strategy for an individual voter.<br>
<br>
The distinction between 'honest voting' and 'strategic voting' may be<br>
confusing if one assumes that the goal of each individual voter is to have<br>
his own greatest preference win. Given the goal of winning, strategic<br>
voting is merely rational and should not be considered somehow dishonest.<br>
It would be irrational for individual voters to ignore the other voters<br>
and for individual voters to thus not attempt to have their own preference<br>
win.<br>
<br>
<br>
1.2. APPROVAL AND RANKING IN SCORE VOTING.<br>
<br>
'Approval voting' is simple yes or no voting for each candidate.<br>
'Approval voting' is a type of score voting in which the range of<br>
permitted scores is limited to two values such as either 0 or 1.<br>
<br>
'Ranking' is used to list relative preferences between candidates in order<br>
for 'preference voting methods'. 'Score voting' uses scores for<br>
expressing absolute preferences for candidates not merely relative<br>
preferences between candidates.<br>
<br>
'Ranked approval voting' is a somewhat contradictory name which I have<br>
given for part of a voting strategy in which votes are expressed as<br>
adjacent scores clustered adjacent to either the highest or lowest scores<br>
in the permitted range. The clustering has elements of both 'approval<br>
voting' and 'preference voting methods'. Examples are given further below<br>
in the context of possible strategies.<br>
<br>
<br>
2. STATEGICALLY POOR VOTING STRATEGIES.<br>
<br>
Strategically poor voting strategies can easily be avoided when<br>
recognised. However, some forms of 'honest voting' may also be<br>
strategically poor voting which is a problem which needs correcting in the<br>
voting method.<br>
<br>
<br>
2.1. WEAK VOTING.<br>
<br>
Weak voting is applying something less than the highest scores in the<br>
possible range for the voter's greatest prefered candidates and something<br>
more than the lowest permitted scores in the range for the voter's least<br>
preferred candidates. Weak voting might be an honest expression of<br>
similarities between candidates but a poor strategy for maximising<br>
individual preferences in the cumulative result of all voters. Other<br>
voters using strong voting, applying the highest possible scores in the<br>
range for greatly prefered candidates and the lowest possible scores in<br>
the range for least prefered candidates, would outvote weak voters.<br>
<br>
<br>
2.1.1. EXAMPLES OF WEAK VOTING.<br>
<br>
2.1.1.1. WEAK VOTING EXAMPLE.<br>
<br>
Score range allows scores from 0 to 10.<br>
Candidates are A, B, C, and D.<br>
300 people vote.<br>
<br>
200 voters score candidates weakly:<br>
A at 7, B at 6, C at 5, and D at 4.<br>
<br>
100 voters score candidates strongly with opposite preference ranking to<br>
other voters:<br>
A at 0, B at 1, C at 9, and D at 10.<br>
<br>
Calculating the averages:<br>
<br>
Candidate A:<br>
((7 score * 200 votes) +<br>
(0 score * 100 votes)) /<br>
300 total votes =<br>
4.6667 average mean score<br>
<br>
Candidate B:<br>
((6 score * 200 votes) +<br>
(1 score * 100 votes)) /<br>
300 total votes =<br>
4.3333 average mean score<br>
<br>
Candidate C:<br>
((5 score * 200 votes) +<br>
(9 score * 100 votes)) /<br>
300 total votes =<br>
6.3333 average mean score<br>
<br>
Candidate D:<br>
((4 score * 200 votes) +<br>
(10 score * 100 votes)) /<br>
300 total votes =<br>
6 average mean score<br>
<br>
Candidates C won. Voters who had used weak scores had some effect on the<br>
outcome in enabling C to beat D. However, voters who had used weak scores<br>
could have enabled their greatest preferred candidate A to win if they had<br>
used strong scores.<br>
<br>
<br>
2.1.1.2. PARTLY CORRECTED WEAK VOTING EXAMPLE.<br>
<br>
Weak voting can be at least partly corrected by simply using the highest<br>
and lowest scores permissible in the range.<br>
<br>
Score range allows scores from 0 to 10.<br>
Candidates are A, B, C, and D.<br>
300 people vote.<br>
<br>
200 voters score candidates with corrections to use the highest and lowest<br>
scores:<br>
A at 10, B at 6, C at 5, and D at 0.<br>
<br>
100 voters score candidates strongly with opposite preference ranking to<br>
the other voters:<br>
A at 0, B at 1, C at 9, and D at 10.<br>
<br>
Calculating the averages:<br>
<br>
Candidate A:<br>
((10 score * 200 votes) +<br>
(0 score * 100 votes)) /<br>
300 total votes =<br>
6.6667 average mean score<br>
<br>
Candidate B:<br>
((6 score * 200 votes) +<br>
(1 score * 100 votes)) /<br>
300 total votes =<br>
4.3333 average mean score<br>
<br>
Candidate C:<br>
((5 score * 200 votes) +<br>
(9 score * 100 votes)) /<br>
300 total votes =<br>
6.3333 average mean score<br>
<br>
Candidate D:<br>
((0 score * 200 votes) +<br>
(10 score * 100 votes)) /<br>
300 total votes =<br>
3.3333 average mean score<br>
<br>
Candidate A won. Correcting weak voting by using the highest and lowest<br>
scores permissible in the range allowed the majority preference for<br>
candidate A to win.<br>
<br>
<br>
2.2. BULLET VOTING.<br>
<br>
Plurality voting could be used as a strategy. If many voters would use<br>
plurality voting as strategy, then a plurality result would be the<br>
unfortunate consequence in the absence of an absolute majority.<br>
<br>
Plurality voting as a strategy instead of a voting method is bullet voting.<br>
<br>
Voters might assign the highest possible score to their greatest prefered<br>
candidate and the lowest possible score to all other candidates. Such a<br>
voting pattern would reduce score voting to common bad plurality voting in<br>
which the candidate with most votes can win despite being opposed by the<br>
majority of voters.<br>
<br>
<br>
2.2.1. EXAMPLES OF BULLET VOTING.<br>
<br>
2.2.1.1. BULLET VOTING EXAMPLE.<br>
<br>
Score range allows scores from 0 to 10.<br>
Candidates are A, B, C, and D.<br>
300 people vote.<br>
<br>
98 voters score candidates:<br>
A at 10, B at 0, C at 0, and D at 0.<br>
<br>
97 voters score candidates:<br>
A at 0, B at 10, C at 0, and D at 0.<br>
<br>
97 voters score candidates:<br>
A at 0, B at 0, C at 10, and D at 0.<br>
<br>
8 voters score candidates:<br>
A at 0, B at 0, C at 0, and D at 10.<br>
<br>
Calculating the averages:<br>
<br>
Candidate A:<br>
((10 score * 98 votes) +<br>
(0 score * 202 votes)) /<br>
300 total votes =<br>
3.2667 average mean score<br>
<br>
Candidate B:<br>
((10 score * 97 votes) +<br>
(0 score * 203 votes)) /<br>
300 total votes =<br>
3.2333 average mean score<br>
<br>
Candidate C:<br>
((10 score * 97 votes) +<br>
(0 score * 203 votes)) /<br>
300 total votes =<br>
3.2333 average mean score<br>
<br>
Candidate D:<br>
((10 score * 8 votes) +<br>
(0 score * 292 votes)) /<br>
300 total votes =<br>
0.2667 average mean score<br>
<br>
Candidate A won for having the highest average mean score despite being<br>
opposed by the majority of voters merely because of a poor strategy to<br>
express only the greatest preference.<br>
<br>
Computer simulations by Warren Smith show that plurality voting is the<br>
best strategy for an individual voter if there are a small number of<br>
voters, <a href="http://www.scorevoting.net/RVstrat3.html" target="_blank">http://www.scorevoting.net/RVstrat3.html</a> . In simulations of a<br>
three candidate election, plurality voting was found the best strategy for<br>
an individual voter if there are not more than ten voters.<br>
<br>
A plurality vote without an absolute majority should be avoided by a rule<br>
that the problem will either be corrected by revoting or the automatic<br>
substitution of required preference ranking.<br>
<br>
<br>
2.2.1.2. PREFERENCE RANKING REQUIREMENT WITH BULLET VOTING EXAMPLE.<br>
<br>
Score range allows scores from 0 to 10.<br>
Candidates are A, B, C, and D.<br>
300 people vote.<br>
<br>
Minimal preference ranks are required for scores preventing multiple 0<br>
scores.<br>
<br>
98 voters score candidates:<br>
A at 10, B at 2, C at 1, and D at 0.<br>
<br>
97 voters score candidates:<br>
A at 0, B at 10, C at 2, and D at 1.<br>
<br>
97 voters score candidates:<br>
A at 1, B at 0, C at 10, and D at 2.<br>
<br>
8 voters score candidates:<br>
A at 2, B at 1, C at 0, and D at 10.<br>
<br>
Calculating the averages:<br>
<br>
Candidate A:<br>
((10 score * 98 votes) +<br>
(0 score * 97 votes) +<br>
(1 score * 97 votes) +<br>
(2 score * 8 votes)) /<br>
300 total votes =<br>
3.6433 average mean score<br>
<br>
Candidate B:<br>
((2 score * 98 votes) +<br>
(10 score * 97 votes) +<br>
(0 score * 97 votes) +<br>
(1 score * 8 votes)) /<br>
300 total votes =<br>
3.9133 average mean score<br>
<br>
Candidate C:<br>
((1 score * 98 votes) +<br>
(2 score * 97 votes) +<br>
(10 score * 97 votes) +<br>
(0 score * 8 votes)) /<br>
300 total votes =<br>
4.2067 average mean score<br>
<br>
Candidate D:<br>
((0 score * 98 votes) +<br>
(1 score * 97 votes) +<br>
(2 score * 97 votes) +<br>
(10 score * 8 votes)) /<br>
300 total votes =<br>
1.2367 average mean score<br>
<br>
Candidate C won. Required preference ordering prevented candidate A for<br>
having the highest average mean score despite being opposed by the<br>
majority of voters merely because of a poor strategy to express only the<br>
greatest preference.<br>
<br>
<br>
3. OPTIMISED VOTING.<br>
<br>
In optimised voting, a voter applies the highest possible score in the<br>
range for the greatest prefered candidate and the lowest possible score in<br>
the range for the least prefered candidate. The difficulty is what to do<br>
about the candidates which are neither the greatest preference nor the<br>
least preference.<br>
<br>
If a voter assigns too high a score to one of the voter's middle<br>
preference candidates, then the high score may help defeat a candidate for<br>
which the voter has a greater preference. If a voter assigns too low a<br>
score to one of the voter's middle preference candidates, then the voter<br>
may help the candidate loose to a candidate for which the voter has a<br>
lesser preference.<br>
<br>
<br>
3.1. SCALED SINCERITY.<br>
<br>
Scaled sincerity voting assigns middle preference candidate scores by<br>
evenly distribution (linear interpolation) across the range of permissible<br>
scores.<br>
<br>
Such an even distribution of scores for candidates would be similar to a<br>
Borda count in which weights (scores) are assigned according to relative<br>
preference rank. The most significant difference is that Borda would not<br>
have a weight of 0 for the lowest ranking preference.<br>
<br>
No analysis of middle preferences except relative ranking by the voter is<br>
needed for scaled sincerity, therefore, the strategy can be used in<br>
circumstances when no other strategy may be determined. In simulations of<br>
millions of election scenarios, scaled sincerity performed at least 91% as<br>
well as the optimum strategy, <a href="http://www.scorevoting.net/RVstrat3.html" target="_blank">http://www.scorevoting.net/RVstrat3.html</a> .<br>
<br>
3.1.1. EXAMPLE OF SCALED SINCERITY.<br>
<br>
Example of scaled sincerity.<br>
<br>
Score range allows scores from 0 to 10.<br>
Candidates are A, B, C, and D.<br>
<br>
The voter has relative preferences A > B > C > D. Scores for the<br>
preferences are evenly distributed as well as can be managed within the<br>
range:<br>
A at 10, B at 7, C at 3, and D at 0.<br>
<br>
<br>
3.2. MEAN BASED THRESHOLDING.<br>
<br>
3.2.1. MEAN BASED THRESHOLDING GENERALLY.<br>
<br>
Mean based thresholding strategy uses the expected utility of the result<br>
for the voter to determine a threshold as a dividing point for optimising<br>
scores either high or low. See the expected utility hypothesis in<br>
Wikipedia, <a href="http://en.wikipedia.org/wiki/Expected_utility_hypothesis" target="_blank">http://en.wikipedia.org/wiki/Expected_utility_hypothesis</a> . The<br>
expected utility may be adjusted by a risk avoidance bias which would<br>
change the threshold. The mean threshold may be adjusted by combining the<br>
expected utility with some expectation or actual knowledge of how other<br>
voters may vote.<br>
<br>
Expected utility of the result can be calculated by the voter first<br>
considering honest scores for middle preference candidates and then<br>
calculating the average mean for the scores assigned for all the<br>
candidates.<br>
<br>
The voter assigns the highest permitted scores to candidates with a first<br>
considered honest score above the calculated threshold and the lowest<br>
permitted scores to candidates equal to or below the threshold.<br>
<br>
Such a mean based thresholding strategy was found to be the most<br>
successful strategy in simulations of millions of elections,<br>
<a href="http://www.scorevoting.net/RVstrat3.html" target="_blank">http://www.scorevoting.net/RVstrat3.html</a> .<br>
<br>
<br>
3.2.1.1. EXAMPLE OF MEAN BASED THRESHOLDING.<br>
<br>
Score range allows scores from 0 to 10.<br>
Candidates are A, B, C, and D.<br>
<br>
In considering honest scores which might be assigned in the absence of<br>
strategy, a voter has the following preferences indicating the voter's<br>
expected utility for each of the candidates:<br>
A at 10, B at 6, C at 2, and D at 0.<br>
<br>
Calculating mean threshold of expected utility:<br>
((10 score * 1 candidate) +<br>
(6 score * 1 candidate) +<br>
(2 score * 1 candidate) +<br>
(0 score * 1 candidate)) /<br>
4 candidates =<br>
4.5 mean threshold<br>
<br>
The voter assigns the highest scores in the permitted range to candidates<br>
with an expected utility above the mean threshold of 4.5. The voter<br>
assigns the lowest scores in the permitted range to candidates with an<br>
expected utility equal to or below the mean threshold of 4.5.<br>
<br>
Approval form with only highest and lowest scores:<br>
A at 10, B at 10, C at 0, and D at 0.<br>
<br>
Ranked approval form with scores adjacent to highest and lowest:<br>
A at 10, B at 9, C at 1, and D at 0.<br>
<br>
<br>
3.2.2. RISK AVOIDANCE BIAS.<br>
<br>
The expected utility may be adjusted by considering a greater voter bias<br>
over risk avoidance. When the risk avoidance bias is sufficiently great,<br>
the risk avoidance has a decisive effect on expected utility of some<br>
candidates and consequently the position of the threshold dividing between<br>
optimising scores high or low.<br>
<br>
Ordinarily one of the great advantages of score voting is that scores can<br>
have a degree of candidate independent absolute value. Adding or<br>
subtracting candidates need not have any effect on how a voter asses<br>
individual candidates, in contrast to preference voting in which<br>
assessments are all relative to other candidates. However, the permitted<br>
range needs to be sufficiently large to account for meaningful differences<br>
between candidates.<br>
<br>
Candidates may exist for which a voter has an indispensably high utility<br>
that alternatives must be avoided or such a horribly low utility that the<br>
horrible candidates must be avoided. At either the high or low end of the<br>
range, the permitted range may be insufficient to include such cases and<br>
have the scale meaningfully differentiate candidates. Scores considered<br>
for candidates should have some sense of relative expected utility in<br>
relation to other candidates.<br>
<br>
For example, the permitted range for scores of 0 to 10 is useful for a<br>
voter to consider the expected utility of candidates A at 10, B at 6, and<br>
C at 0. However, candidate D may be indispensably valuable and may have<br>
an expected utility of 1,000 which is outside the permitted range.<br>
Alternatively, candidate D may have a horribly low value to be avoided<br>
that the candidate may have an expected value of -1000. Incorporating<br>
indispensable D at the top of the range with score 10 should squash the<br>
scale for the other candidates to scores near 0. Alternatively,<br>
incorporating horrible D at bottom of the range with score 0 should squash<br>
the scale for the other candidates to scores near 10.<br>
<br>
Distance between extreme alternatives within the permitted range should be<br>
maximised for risk avoidance. If some candidates are indispensable, they<br>
should have the highest permitted scores and all other candidates should<br>
have the lowest permitted scores to avoid the others. If some candidates<br>
are indispensable, they should have the highest permitted scores and all<br>
other candidates should have the lowest permitted scores to avoid the<br>
others.<br>
<br>
If there is only one indispensable candidate or only one horrible<br>
candidate for the voter, then the optimal voting strategy becomes a form<br>
of bullet (plurality) voting as described further above in section 2.2.<br>
In such a circumstance, bullet voting would not be a poor strategy as<br>
described above, but the optimal strategy for the voter.<br>
<br>
<br>
3.2.2.1. EXAMPLES OF RISK AVOIDANCE.<br>
<br>
[Unlike other cases, 5 candidates may better show what happens to<br>
individual candidates.]<br>
<br>
<br>
3.2.2.1.1. INDISPENSABLE CANDIDATES RISK AVOIDANCE EXAMPLE.<br>
<br>
Score range allows scores from 0 to 10.<br>
Candidates are A, B, C, D, and E.<br>
<br>
Either candidate A or B are indispensable to the voter with A preferred to B.<br>
<br>
In considering honest scores which might be assigned in the absence of<br>
strategy and ignoring the range restriction, a voter has the following<br>
preferences indicating the voter's expected utility for each of the<br>
candidates:<br>
A at 1000, B at 700, C at 10, D at 6, and E at 0.<br>
<br>
Calculating mean threshold of expected utility:<br>
((1000 score * 1 candidate) +<br>
(700 score * 1 candidate) +<br>
(10 score * 1 candidate) +<br>
(6 score * 1 candidate) +<br>
(0 score * 1 candidate)) /<br>
5 candidates =<br>
343.2 mean threshold<br>
<br>
The voter assigns the highest scores in the permitted range to candidates<br>
with an expected utility above the mean threshold of 343.2. The voter<br>
assigns the lowest scores in the permitted range to candidates with an<br>
expected utility equal to or below the mean threshold of 343.2.<br>
<br>
Approval form with only highest and lowest scores:<br>
A at 10, B at 10, C at 0, D at 0, and E at 0.<br>
<br>
Ranked approval form with scores adjacent to highest and lowest:<br>
A at 10, B at 9, C at 2, D at 1, and E at 0.<br>
<br>
<br>
3.2.2.1.2. HORRIBLE CANDIDATES RISK AVOIDANCE EXAMPLE.<br>
<br>
Score range allows scores from 0 to 10.<br>
Candidates are A, B, C, D, and E.<br>
<br>
Candidates D and E are both horrible to the voter with D preferred to E.<br>
<br>
In considering honest scores which might be assigned in the absence of<br>
strategy and ignoring the range restriction, a voter has the following<br>
preferences indicating the voter's expected utility for each of the<br>
candidates:<br>
A at 10, B at 6, C at 0, D at -700, and E at -1000.<br>
<br>
Calculating mean threshold of expected utility:<br>
((10 score * 1 candidate) +<br>
(6 score * 1 candidate) +<br>
(0 score * 1 candidate) +<br>
(-700 score * 1 candidate) +<br>
(-1000 score * 1 candidate)) /<br>
5 candidates =<br>
-336.8 mean threshold<br>
<br>
The voter assigns the highest scores in the permitted range to candidates<br>
with an expected utility above the mean threshold of -336.8. The voter<br>
assigns the lowest scores in the permitted range to candidates with an<br>
expected utility equal to or below the mean threshold of -336.8.<br>
<br>
Approval form with only highest and lowest scores:<br>
A at 10, B at 10, C at 10, D at 0, and E at 0.<br>
<br>
Ranked approval form with scores adjacent to highest and lowest:<br>
A at 10, B at 9, C at 8, D at 1, and E at 0.<br>
<br>
<br>
3.2.2.1.3. INDISPENSABLE AND HORRIBLE CANDIDATES RISK AVOIDANCE EXAMPLE.<br>
<br>
Score range allows scores from 0 to 10.<br>
Candidates are A, B, C, D, and E.<br>
<br>
Candidate A is indispensable to the voter with A preferred to B.<br>
Candidates D and E are both horrible to the voter with D preferred to E.<br>
<br>
In considering honest scores which might be assigned in the absence of<br>
strategy and ignoring the range restriction, a voter has the following<br>
preferences indicating the voter's expected utility for each of the<br>
candidates:<br>
A at 1000, B at 6, C at 0, D at -700, and E at -1000.<br>
<br>
Adjusting the scale for the expected utilities to a scale of non-negative<br>
integers:<br>
A at 2000, B at 1006, C at 1000, D at 300, and E at 0.<br>
<br>
Calculating mean threshold of expected utility:<br>
((1000 score * 1 candidate) +<br>
(6 score * 1 candidate) +<br>
(0 score * 1 candidate) +<br>
(-700 score * 1 candidate) +<br>
(-1000 score * 1 candidate)) /<br>
5 candidates =<br>
-138.8 mean threshold<br>
<br>
The voter assigns the highest scores in the permitted range to candidates<br>
with an expected utility above the mean threshold of -138.8. The voter<br>
assigns the lowest scores in the permitted range to candidates with an<br>
expected utility equal to or below the mean threshold of -138.8.<br>
<br>
Approval form with only highest and lowest scores:<br>
A at 10, B at 10, C at 10, D at 0, and E at 0.<br>
<br>
Ranked approval form with scores adjacent to highest and lowest:<br>
A at 10, B at 9, C at 8, D at 1, and E at 0.<br>
<br>
<br>
3.2.3. THRESHOLD ADJUSTMENT.<br>
<br>
3.2.3.1. EXPECTATION OF OTHER VOTERS' PATTERNS.<br>
<br>
If an expectation of the candidate scoring patterns for other voters is<br>
known, then that expectation can be incorporated into the threshold<br>
calculation. See the threshold strategy as described by Clay Shentrup's<br>
organisation, The Center for Election Science,<br>
<a href="http://www.electology.org/threshold" target="_blank">http://www.electology.org/threshold</a> .<br>
<br>
<br>
3.2.3.2. KNOWLEDGE OF OTHER VOTERS' PATTERNS.<br>
<br>
If there is actual knowledge of how other voters have already scored<br>
candidates in an ongoing election, then that knowledge can be incorporated<br>
into the threshold calculation. We should have knowledge of how other<br>
voters have already scored candidates during the voting period for<br>
revoting to consensus. However, consensus discussion should help everyone<br>
optimise votes more than a simple threshold calculation for individual<br>
voters.<br>
<div><div></div><div class="h5"><br>
<br>
Thomas Dukleth<br>
Agogme<br>
109 E 9th Street, 3D<br>
New York, NY 10003<br>
USA<br>
<a href="http://www.agogme.com" target="_blank">http://www.agogme.com</a><br>
+1 212-674-3783<br>
<br>
<br>
</div></div></blockquote></div><br><br clear="all"><br>-- <br><b><font color="#333333">Clay Shentrup</font></b><div><b><font color="#333333">Secretary, Director</font></b></div><div><b><font color="#333333">The Center for Election Science</font></b></div>
<div><b><font color="#333333"><a href="http://www.electology.org/" target="_blank">http://www.electology.org/</a></font></b></div><div><b><font color="#333333">206.801.0484</font></b></div><br>