User:BetterVotingAdvocacy/Negative vote-counting approach for pairwise counting: Difference between revisions

*The negative counting approach would require at least 56,181 marks for any implementation, for an average of '''6.25''' marks per ballot.

*The semi-negative approach would require at least 39,114 marks (avg = '''4.35''' marks/ballot).

*The regular approach would require at least 73,669 marks ('''8.2''' marks/ballot).

** If counting 1st choices separately from all other ranks, then it would only require 46,642 marks ('''5.19''' marks/ballot).

*[[FPTP]]: ~8,980 marks (''1'' mark/ballot)

*[[RCV]]: 12,309 marks (''1.37'' marks/ballot. 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>)

**Approval voting: ~20,000 marks (''2.22'' marks/ballot<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

**Score voting: ~20,000 to ~30,000 marks (''2.22'' to ''3.34'' marks/ballot)

*Negative counting approach requires at least 4,482 marks ('''18''' marks/ballot).

*Semi-negative approach requires at least 3,208 marks ('''12.88''' marks/ballot).

*Regular approach requires at least 8,223 marks ('''33.02''' marks/ballot).

**If 1st choices are counted separately, then this only requires 5,982 marks ('''24.02''' marks/ballot).

*[[RCV]]: 354 marks (average of ''1.42'' marks/ballot. 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>)

**Approval voting: 996 marks (''4'' marks/ballot)

**Score voting: 1245 marks (''5'' marks/ballot)

*Negative counting approach requires at least 95 marks ('''2.85''' marks/ballot).

*Semi-negative approach requires at least 69 marks ('''2.02''' marks/ballot).

*Regular approach requires at least 146 marks ('''4.29''' marks/ballot).

**If 1st choices are counted separately, then this only requires 88 marks ('''2.58''' marks/ballot).

* FPTP: 34 marks (''1'' mark/ballot)

* Score voting: 132 marks (''3.88'' marks/ballot)

** Score voting with averages: 134 marks (''3.94'' marks/ballot). 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)