User:BetterVotingAdvocacy/Negative vote-counting approach for pairwise counting: Difference between revisions
User:BetterVotingAdvocacy/Negative vote-counting approach for pairwise counting (view source)
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Based on the above table:
*The negative counting approach would require at least 56,181 marks for any implementation, for an average of '''6.25''' marks per ballot (=1.25 marks/ballot/number of non-write-in candidates).
**This assumes last-ranked candidates weren't counted with any marks (which means write-in candidates' pairwise matchups wouldn't have been counted accurately).
**The calculation is (1*1481 + 3*1912 + 6*1799 + 10*873 + 10*2944).
*The semi-negative approach would require at least 39,114 marks (avg = '''4.35''' marks/ballot or 0.87 marks/ballot/candidate).
**Calculation: (1*1481+3*1912+5*1799+6*873+6*2944). This is found by observing that, for example, when a voter ranked 2 candidates, it was most efficient to count their 2nd choice with the negative approach rather than the regular approach, but when they ranked their 3rd choice, it was faster to use the regular approach (i.e. mark that they're ranked above 2 candidates) rather than the negative approach (3 values, because the candidate is ranked below 2 candidates, and a 3rd mark has to be made to show that they're ranked by the voter).
*The regular approach would require at least 73,669 marks ('''8.2''' marks/ballot or 1.64 marks/ballot/candidate).
** If counting 1st choices separately from all other ranks, then it would only require 46,642 marks ('''5.19''' marks/ballot or 1.038 marks/ballot/candidate).
***Calculation: (1*1481 + 4*1912 + 6*1799 + 7*873 + 7*2944)
**This is if miscounting write-ins' matchups, which is the usual way to treat them.
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Also of interest may be the comparison to non-pairwise counting methods. The following are rough estimates for the number of marks:
*[[FPTP]]: ~8,980 marks (''1'' mark/ballot or 0.2 marks/ballot/candidate)
*[[RCV]]: 12,309 marks (''1.37'' marks/ballot or 0.274 m/b/c. Derived by counting 8,980 1st choices + 3,329 vote transfers<ref>{{Citation|last=|first=|title=2009 Burlington mayoral election|date=2020-05-05|url=https://en.wikipedia.org/wiki/2009_Burlington_mayoral_election#Results|work=Wikipedia|volume=|pages=|language=en|access-date=2020-05-20}}</ref>)
*Hypothetical:
**Approval voting: ~20,000 marks (''2.22'' marks/ballot or 0.444 m/b/c<ref>{{Cite web|url=https://rangevoting.org/Burlington.html|title=RangeVoting.org - Burlington Vermont 2009 IRV mayoral election|last=|first=|date=|website=rangevoting.org|url-status=live|archive-url=|archive-date=|access-date=2020-05-16|quote=We do not know who Range & Approval voting would have elected because we only have rank-order ballot data – depending on how the voters chose their "approval thresholds" or numerical range-vote scores, they could have made any of the Big Three win (also Smith). However it seems likely they would have elected Montroll. Here's an analysis supporting that view: Suppose we assume that voters who ranked exactly one candidate among the big three would have approved him alone; voters who ranked exactly two would have approved both, and voters who ranked all three would have approved the top-two a fraction X of the time (otherwise approve top-one alone). The point of this analysis, suggested by Stephen Unger, is that voters were allowed to vote "A>B," which while mathematically equivalent to "A>B>C" among the three candidates A,B,C, was psychologically different; by "ranking" a candidate versus "leaving him unranked" those voters in some sense were providing an "approval threshhold." Then the total approval counts would be
Montroll=4261+1849X, Kiss=3774+1035X, and Wright=3694+741X.
Note that Montroll is the most-approved (and Wright the least-approved) regardless of the value of X for all X with 0≤X≤1.}}</ref>)
**Score voting: ~20,000 to ~30,000 marks (''2.22'' to ''3.34'' marks/ballot or 0.444 to 0.668 m/b/c)
===Evanston, IL 2020 Democrat endorsement===
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*Negative counting approach requires at least 4,482 marks ('''18''' marks/ballot or 1.63 m/b/c).
**Calculation: (48 + 3*35 + 6*22 + 10*39 + 15*25 + 21*16 + 28*10 + 36*6 + 45*4 + 55*4 + 55*40)
*Semi-negative approach requires at least 3,208 marks ('''12.88''' marks/ballot or 1.17 m/b/c).
**Calculation: (48 + 3*35 + 6*22 + 10*39 + 15*25 + 20*16 + 24*10 + 27*6 + 29*4 + 30*4 + 30*40)
*Regular approach requires at least 8,223 marks ('''33.02''' marks/ballot or 3 m/b/c).
**If 1st choices are counted separately, then this only requires 5,982 marks ('''24.02''' marks/ballot or 2.18 m/b/c).
***Calculation: (1*48 + 10*35 + 18*22 + 25*39 + 31*25 + 36*16 + 40*10 + 43*6 + 45*4 + 46*4 + 46*40)
**Calculation: (10*48 + 19*35 + 27*22 + 34*39 + 40*25 + 45*16 + 49*10 + 52*6 + 54*4 + 55*4 + 55*40)
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====Non-pairwise methods====
*[[RCV]]: 354 marks (average of ''1.42'' marks/ballot or 0.129 m/b/c. It is derived by counting 249 voters' 1st choices + 105 votes transferred throughout<ref>https://i0.wp.com/evanstondems.com/wp-content/uploads/2020/02/RCVPrez-Results.png?fit=1024%2C341&ssl=1</ref>)
*Hypothetical:
**Approval voting: 996 marks (''4'' marks/ballot or 0.36 m/b/c)
**Score voting: 1245 marks (''5'' marks/ballot or 0.45 m/b/c)
===2017 Green Party of Utah co-chair election===
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*Negative counting approach requires at least 95 marks ('''2.85''' marks/ballot or 0.69 m/b/c).
**Calculation: ([14+15+2] + [[2*12 + 3*7] + [2*2*1]] + [3*5])
*Semi-negative approach requires at least 69 marks ('''2.02''' marks/ballot or 0.5 m/b/c).
**Calculation: ([14+15+2] + [[2*12 + 1*7] + [2*1]] + [1*5])
*Regular approach requires at least 146 marks ('''4.29''' marks/ballot or 1.07 m/b/c).
**If 1st choices are counted separately, then this only requires 88 marks ('''2.58''' marks/ballot or 0.64 m/b/c).
***Calculation: ([1*14 + 2*15 + 3*2] + [[2*12 + 1*7] + [2*1]] + [1*5])
**Calculation: ([3*14 + 4*15 + 3*2] + [[2*12 + 1*7] + [2*1]] + [1*5])
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====Non-pairwise methods====
* FPTP: 34 marks (''1'' mark/ballot or 0.25 m/b/c)
* Score voting: 132 marks (''3.88'' marks/ballot or 0.97 m/b/c)
** Score voting with averages: 134 marks (''3.94'' marks/ballot or 0.98 m/b/c). This is because there is one voter who explicitly scored 2 candidates at 0, so they would've required an additional 2 marks to count.
* RCV: ''At most'' 102 marks (''3'' marks/ballot or 0.75 m/b/c)
** There were 34 1st choices, and at most all ballots have to transfer their votes twice before only 2 candidates remain. Note: This is a ''non-tight'' upper bound.
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