Proportional 3RD (3-rating delegated) voting: Difference between revisions
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imported>Homunq No edit summary |
imported>Homunq (N^2 summable version.) |
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** Usually, the safest strategy is to rate just your favorite as "good". If you trust that favorite's ratings, you can leave the others blank; otherwise, you can explicitly divide the others between "OK" and "bad". |
** Usually, the safest strategy is to rate just your favorite as "good". If you trust that favorite's ratings, you can leave the others blank; otherwise, you can explicitly divide the others between "OK" and "bad". |
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* Votes are tallied for each pair of candidates X and Y, to see what portion of ballots that rate X "Good" will rate Y at least "OK". |
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** A ballot that rates N different candidates "good" only counts as 1/N in each of these tallies. |
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** For example, suppose that there were three candidates: X, Y, and Z. If the three ballots were "Good, OK, Bad", "Good, Good, Bad", and "Good, Bad, Good", then the XY tally would be 1+.5+.5=2 X, votes of which 1+.5=1.5 rate Y at least OK. |
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* These tallies are then used in a Single Transferrable Voting-like (STV-like) procedure to find the winners. |
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⚫ | ** This is a process which finds winning candidates and assigns them each an equal amount of votes, while trying to ensure that each vote is assigned to a candidate it rates as highly as possible. ** Each vote is assigned to a candidate or candidates it rates at least "OK". To get assignments to balance, votes may be assigned in fractions; for instance, half to one candidate and half to another. |
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== STV process == |
== STV process == |
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# Find winners and transfer leftovers |
# Find winners and transfer leftovers |
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#: If V is the total number of valid (non-exhausted) votes, and S is the number of seats, then a “quota” is defined as Q=V/(S+1). This ensures that each full “quota” of voters will get a seat, with less than one “quota” of vote left unrepresented even though they still have a valid preference. |
#: If V is the total number of valid (non-exhausted) votes, and S is the number of seats, then a “quota” is defined as Q=V/(S+1). This ensures that each full “quota” of voters will get a seat, with less than one “quota” of vote left unrepresented even though they still have a valid preference. |
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#: Any candidate with a full quota of points at any time is elected. If their winning point total is W>Q, then the leftover |
#: Any candidate with a full quota of points at any time is elected. If their winning point total is W>Q, then the leftover points T=(W-Q) are transferred. |
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# Eliminate candidate with lowest total and transfer votes |
# Eliminate candidate with lowest total and transfer votes |
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#: When transferring any portion of a vote |
#: When transferring any portion of a vote that originally went to candidate X, it is split among the other candidates who were rated above "bad" by the voters who rated "X" good. Each other candidate Y gets a portion equal to Tally(XY)*Tally(YY). |
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# If there are still seats to fill, repeat from step 2. |
# If there are still seats to fill, repeat from step 2. |
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== Example == |
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Suppose that there were three candidates: X, Y, and Z, for two seats. Say the only three ballots were "Good, OK, Bad", "Good, Good, Bad", and "Good, Bad, Good". |
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Quota to win: Q=V/(S+1)=3/(2+1)=3/3=1 |
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Initial tallies: 2, .5, .5. |
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X wins the first seat. Transfer T=(W-Q)=2-1=1 point. |
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Transfers to Y will be proportional to TXY=Tally(XY)*Tally(YY)=1.5 * .5 =.75 |
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Transfers to Z will be proportional to TXZ=Tally(XZ)*Tally(ZZ)=.5 * .5 =.25 |
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Thus, Y gets T*TXY/(TXY+TXZ)=1*.75/(.75+.25)=.75/1=.75 transferred points, for a total of .5+.75=1.25. |
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Z gets T*TXZ/(TXY+TXZ)=1*.25/(.75+.25)=.25/1=.25 transferred points, for a total of .5+.25=.75. |
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Y has over one quota, so they win. Both seats are now filled, so the election is over. |
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If the election were not over, you would have to transfer .25 votes for Y. Of those, .5/1.25=40% of .25=.1 originally went to Y, while the other .15 originally went to X. The .15 that went to X now go to Z in the amount T*TXZ/(TXZ)=.15*.25/(.25)=.15; that is to say, since only Z remains, they all go to Z. The .1 that originally went to Y are now exhausted, because Tally(YZ) is 0; there is no overlap between voters who rated Y as "good" and those who rated Z at least "OK". So Z ends up with a tally of .75+.15=.9. |
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If, due to exhausted votes, no candidate has a quota but there are still M seats to fill, the top M candidates get the remaining seats, with no more vote transfers. |
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== Delegation (rules for filling in blank ratings) == |
== Delegation (rules for filling in blank ratings) == |
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Whenever a voter leaves a blank, it is filled in by the ratings of the voter's favorite candidates. |
Whenever a voter leaves a blank, it is filled in by the ratings of the voter's favorite candidates. |
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* That is, a blank for candidate |
* That is, a blank for candidate Y counts as "OK" in the XY tally if Y was rated "OK" by X. |
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(Note that the above ballot format and rules are basically the same as those of [3-2-1 voting], a single-winner, nonproportional voting method.) |
(Note that the above ballot format and rules are basically the same as those of [3-2-1 voting], a single-winner, nonproportional voting method.) |