The Numbers of STV and Proportional Representation

A working example to show how FPTP works and how single voting and STV are better

Say 100 votes overall

five parties, each with multiple candidates, and two independent candidates.

FPTP:

five districts INDEPENDENTS

Red Blue Orange Green Black Drew Dana

Central 8 4 2 2 2 18

East 7 4 3 2 1 4 21

West 7 5 3 2 2 4 23

North 7 6 3 2 1 19

South 6 6 3 2 2 19

35 25 14 10 8 4 4 100

Red wins every seat because the Red Candidate in each riding had more votes than any other single candidate.

Block Voting

But if we group the five separate districts into just one district and bring in Block Voting give each voter five votes assuming any vote leakage is balanced by equal and opposite vote leakage)

we see this

one district INDEPENDENTS

Red Blue Orange Green Black Drew Dana

candidates 5 5 4 4 2 1 1

voters 35 25 14 10 8 4 4 100

party totals 175 125 56 40 16 4 4

vote tally of each candidate (at most)

35 25 14 10 8 4 4

each Red candidate takes 35 votes, which is more than any other candidate so they are all five elected.

same results as FPTP.

But if each voter merely has one vote, we see widely different results:

one district INDEPENDENTS

Red Blue Orange Green Black Drew Dana

candidates 3 3 2 1 1 1 1

voters 35 25 14 10 8 4 4 100

party totals 35 25 14 10 8 4 4

vote tally of each candidate (at most)

35 25 14 10 8 4 4

candidates vote tallies

15-12-8 10-9-6 8-6 10 8 4 4

(only 12 candidates, compared to the 22 under FPTP, because parties under SNTV need to constrain their size of their slates and having one district makes the party strategizing easier.)

if votes are distributed like that, then order of election is:

Red 15, Red 12, Blue 10, Green 10, Blue 9.

Red takes only two seats compared to five under FPTP and Block Voting.

Blue takes two seats, and

a third party is also represented -- Green with one seat.

a much more balanced result than the Red's total sweeps under FPTP and Block Voting.

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STV

Let's see what happens if each voter has just one vote but it is a transferable vote.

(we assume that a vote for any party candidate is transferred if necessary equally to other candidates of the same party;

vote for the Black party candidate go to Orange,

vote for Orange goes to Orange then to Red candidates

Drew and Dana votes are to be transferred to Green party candidate, then to Orange

(transfers end when candidate achieves quota so no surplus votes are used in this example)

one district INDEPENDENTS

Red Blue Orange Green Black Drew Dana

candidates 3 3 2 1 1 1 1

voters 35 25 14 10 8 4 4 100

party totals 35 25 14 10 8 4 4

vote tally of each candidate (at most)

35 25 14 10 8 4 4

candidates vote tallies

17-10-8 10-9-6 8-6 10 8 4 4

(under STV, I have parties running the same number of candidates as under SNTV.

The transferable votes means parties do not need to be as careful is constraining the size of their slates but I used the SNTV slates to make the example appear cleaner.)

100 votes five to be elected quota (Droop) is 17

Rounds of counting 1 2 3 4 5

Red candidate Terry 17 elected

Red candidate Chris 10 +7 17 elected

Blue candidate Valentine 10 +3 13 (elected)

Green candidate Taylor 10 +8 18 elected

Blue candidate Casey 9 +3 12

Red candidate Sid 8 -8 0

Orange candidate Bob 8 +6 14 +3 17 elected

Black candidate Jo 8 -8 0

Blue candidate Sidney 6 -6 0

Orange candidate Blake 6 -6 0

Drew 4 -4 0

Dana 4 -4 0

total valid votes 100

exhausted 5 6

in Round 6, Casey is declared defeated,

this leaves just Valentine to fill the last seat.

Thus elected are: two Red, 1 Blue, 1 Orange, 1 Green

of the five in winning positions in the first round, only Casey was not elected.

Casey's 12 votes and the 6 exhausted votes were the only ones not used to elect someone.

Effective votes 4 quota-winners X 17 = 68, plus Valentine's 13 votes = 81

81 percent of valid voters were used to elect someone, much larger portion than the 35 votes used to elect all the winners under FPTP and the vote cast by just 35 voters under Block Voting.

Valentine was elected with only a partial quota but had more votes than any defeated candidate.

Orange party did not have enough votes on its own to achieve quota,

but with out-of-party help from Drew and Dana, Orange candidate Bob did achieve quota and was elected.

Thus elected are: two Red, 1 Blue, 1 Orange, 1 Green

This result is very close to that produced by basic single voting

but with vote transfers, Blue took one fewer seats, and Orange finally received representation.

every party except Black party received representation.

The voters who supported Black's Jo, and those who initially supported Dana and Drew, all saw most of their votes go to elect others who were marked as back-up preferences.

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