1 surplus allocation
1.1 random subset
1.2 hare
1.3 cincinnati
1.4 wright
1.5 hare-clark
1.6 gregory
surplus allocation
to minimize wasted votes, surplus votes transferred other candidates. number of surplus votes known; none of various allocation methods universally preferred. alternatives exist deciding votes transfer, how weight transfers, receives votes , order in surpluses 2 or more winners transferred. reallocation occurs when candidate receives more votes necessary meet quota. excess votes reallocated still other candidates.
random subset
some surplus allocation methods select random vote sample. sometimes, ballots of 1 elected candidate manually mixed. in cambridge, massachusetts, votes counted 1 precinct @ time, imposing spurious ordering on votes. prevent transferred ballots coming same precinct, every
n
{\displaystyle n}
th ballot selected,
1
n
{\displaystyle {\begin{matrix}{\frac {1}{n}}\end{matrix}}}
fraction selected.
hare
reallocation ballots drawn @ random transferred. in manual count of paper ballots, easiest method implement; close thomas hare s original 1857 proposal. used in universal suffrage elections in republic of ireland. exhausted ballots cannot reallocated, , therefore not contribute candidate.
cincinnati
reallocation ballots drawn @ random of candidate s votes. method more hare representative, , less suffer exhausted ballots. starting point counting arbitrary. under recount same sample , starting point used in recount (i.e., recount must check mistakes in original count, , not second selection of votes).
hare , cincinnati have same effect first-count winners, since winners votes in last batch received hare surplus drawn.
wright
the wright system reiterative linear counting process on each candidate s exclusion count reset , recounted, distributing votes according voters nominated order of preference, excluding candidates removed count if had not nominated.
for each successful candidate exceeds quota threshold, calculate ratio of candidate s surplus votes (i.e., excess on quota) divided total number of votes candidate, including value of previous transfers. transfer candidate s votes each voter s next preferred hopeful. increase recipient s vote tally product of ratio , ballot s value previous transfer (1 initial count.)
the uk s electoral reform society recommends method. every preference continues count until choices on ballot have been exhausted or election complete. main disadvantage given large numbers of votes, candidates and/or seats, counting administratively burdensome manual count due number of interactions. not case use of computerised distribution of preference votes.
from may 2011 june 2011, proportional representation society of australia reviewed wright system noting:
while believe wright system advocated mr. anthony van der craats system sound , has technical advantages on prsa 1977 rules, nevertheless sort of elections (the prsa) conduct, these advantages not outweigh considerable difficulties in terms of changing our (the prsa) rules , associated software , explaining these changes our clients. nevertheless, if new software written can used test wright system on our election counts, software read comma separated value file (or openstv blt files), prepared consider further testing of wright system.
hare-clark
this variation on original hare method used random choices. used in elections in australia. allows votes same ballots repeatedly transferred. surplus value calculated based on allocation of preference of last bundle transfer. last bundle transfer method has been criticised being inherently flawed in 1 segment of votes used transfer value of surplus votes denying voters contributed candidate s surplus in surplus distribution. in following explanation, q quota required election.
repeat 3–5 until winners fill seats, or ballots exhausted.
if more winners needed, declare loser hopeful fewest votes, recompute q , repeat 1, ignoring preferences loser.
example: if q 200 , winner has 272 first-choice votes, of 92 have no other hopeful listed, surplus 72, ratio 72/(272−92) or 0.4. if 75 of reassigned 180 ballots have hopeful x second-choice, , if x has 190 votes, x becomes winner, surplus of 20 next round, if needed.
the australian variant of step 7 treats loser s votes though surplus votes. redoing whole method prevents perhaps significant way of gaming system – voters put first candidate sure eliminated early, hoping later preferences have more influence on outcome.
gregory
another method, known senatorial rules (after use seats in irish senate elections), or gregory method (after inventor in 1880, j.b. gregory of melbourne) eliminates randomness. instead of transferring fraction of votes @ full value, transfer votes @ fractional value.
in above example, relevant fraction
75
272
−
92
=
4
10
{\displaystyle \textstyle {\frac {75}{272-92}}={\frac {4}{10}}}
. note part of 272 vote result may earlier transfers; e.g., perhaps y had been elected 250 votes, 150 x next preference, previous transfer of 30 votes 150 ballots @ value of
1
5
{\displaystyle \textstyle {\frac {1}{5}}}
. in case, these 150 ballots retransferred compounded fractional value of
1
5
×
4
10
=
4
50
{\displaystyle \textstyle {\frac {1}{5}}\times {\frac {4}{10}}={\frac {4}{50}}}
.
in republic of ireland, gregory used senate, franchise restricted approximately 1,500 councillors, members of parliament , national university of ireland , university of dublin graduates 6 of seats. however, in northern ireland beginning in 1973, gregory used stv elections, 7 fractional transfers (in 8-seat district council elections), , 700,000 votes counted (in 3-seat european parliament elections).
an alternative means of expressing gregory in calculating surplus transfer value applied each vote is
surplus transfer value
=
(
total value of candidate s votes
−
quota
total value of candidate s votes
)
×
value of each vote
{\displaystyle {\text{surplus transfer value}}=\left({{{\text{total value of candidate s votes}}-{\text{quota}}} \over {\text{total value of candidate s votes}}}\right)\times {\text{value of each vote}}}
^ single transferable vote rules uk electoral reform society
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