1 quota
1.1 hare quota
1.2 droop quota
1.2.1 example
quota
the quota (sometimes called threshold) number of votes candidate must receive elected. hare quota , droop quota commonly used determine quota.
hare quota
when thomas hare conceived version of single transferable vote, envisioned using quota:
in unlikely event each successful candidate receives same number of votes, not enough candidates can meet quota , fill available seats in 1 count. last candidate cannot not meet quota, , may fairer eliminate candidate.
to avoid situation, common instead use droop quota, lower hare quota.
droop quota
the common quota formula droop quota, given as:
droop produces lower quota hare. if each ballot has full list of preferences, droop guarantees every winner meets quota rather being elected last remaining candidate after lower candidates eliminated. fractional part of resulting number, if any, dropped (the result rounded down next whole number.)
it necessary allocate enough votes ensure no other candidate still in contention win. leaves 1 quota s worth of votes unallocated, counting these not alter outcome.
droop whole-number threshold (a) majority of voters can guaranteed elect majority of seats when there odd number of seats; (b) fixed number of seats.
each winner s surplus votes transfer other candidates according remaining preferences, using formula s/t*p, s number of surplus votes transferred, t total number of transferable votes (that have second preference) , p number of second preferences given candidate. meek s counting method recomputes quota on each iteration of count.
example
two seats need filled among 4 candidates: andrea, brad, carter, , delilah. 57 voters cast ballots following preference orderings:
the quota calculated
57
2
+
1
+
1
=
20
{\displaystyle {57 \over 2+1}+1=20}
.
in first round, andrea receives 40 votes , delilah 17. andrea elected 20 surplus votes. ignoring how votes valued example, 20 votes reallocated according second preferences. 12 of reallocated votes go carter, 8 brad.
as none of hopefuls have reached quota, brad, candidate fewest votes, excluded. of votes have carter next-place choice, , reallocated carter. gives carter 20 votes , fills second seat.
thus:
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