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Proportional 3RD (3-rating delegated) voting: Difference between revisions
Proportional 3RD (3-rating delegated) voting (view source)
Revision as of 15:36, 28 June 2017
, 6 years agoN^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".
* 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".
The basic vote-counting process has 4 steps (based on STV, Single Transferrable Voting). 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. Votes may be assigned in fractions; for instance, half to one candidate and half to another.▼
** A ballot that rates N different candidates "good" only counts as 1/N in each of these tallies.
** 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.
* These tallies are then used in a Single Transferrable Voting-like (STV-like) procedure to find the winners.
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== STV process ==
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# Find winners and transfer leftovers
#: 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.
#: Any candidate with a full quota of points at any time is elected. If their winning point total is W>Q, then the leftover
# Eliminate candidate with lowest total and transfer votes
#: When transferring any portion of a vote
# If there are still seats to fill, repeat from step 2.
== Example ==
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".
Quota to win: Q=V/(S+1)=3/(2+1)=3/3=1
Initial tallies: 2, .5, .5.
X wins the first seat. Transfer T=(W-Q)=2-1=1 point.
Transfers to Y will be proportional to TXY=Tally(XY)*Tally(YY)=1.5 * .5 =.75
Transfers to Z will be proportional to TXZ=Tally(XZ)*Tally(ZZ)=.5 * .5 =.25
Thus, Y gets T*TXY/(TXY+TXZ)=1*.75/(.75+.25)=.75/1=.75 transferred points, for a total of .5+.75=1.25.
Z gets T*TXZ/(TXY+TXZ)=1*.25/(.75+.25)=.25/1=.25 transferred points, for a total of .5+.25=.75.
Y has over one quota, so they win. Both seats are now filled, so the election is over.
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.
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.
== 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.
* That is, a blank for candidate
(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.)
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