STV is sometimes accused of being random.
The random-ness - what random-ness there is - comes in when subsequent (later) preferences on the transferred ballots are considered for later transfers, if they are. I'll try to show this:
Sample STV election Quota is Droop and three are elected. DM of three is low. DM of more than three is more certain to produce mixed representation but this 3-seat demonstration election shows the process and where the effect of random-ness might start to bite.
The random-ness - what random-ness there is - comes in when subsequent (later) preferences on the transferred ballots are considered for later transfers, if they are. This demonstration election shows this. Pretend election where three are elected, five candidates Vote counting and transfers may look like this (as explained below): 1 stage 2 stage 3 stage 4 stage A 150 -60 90 elected elected B 62 0 62 + 2 64 +? (64+?) C 61 +40 101 -11 90 elected D 47 +10 57 +6 63 +? (63+?) E 38 +10 48 +3 51 -51 0 total 358
Stage 1
A is elected as she has quota.
Stage 2 Quota is 90 A's surplus is 60 Votes for candidate A (elected) are marked: 100 A/C (where A is the first preference and C is the second preference) 25 A/D 25 A/E C gets 40 votes from A D gets 10 votes from A E gets 10 vote from A The 40 and 10 and 10 are noted in the vote count table above. C is elected.
Stage 3 C's surplus votes -- 11 -- are transferred. When A surplus was transferred, later preferences were not considered but now the third preference on those transferred ballots are considered. They are now seen to be as per the following table. (just looking at next usable preference, ignoring any marked A) C's votes by third preference overall numbers proportion actual of C's votes converted transfers in A's surplus as per 3rd preference. to the 11 surplus whole vote B 10 10 20 2.2 2 D 31 24 55 6 6 E 20 6 26 2.8 3 total 61 40 101 11 When this 11-vote transfer is put in the vote count table above, we see that no one is elected in 3rd Stage. So next stage must involve elimination of least-popular candidate. 4th Stage E, being the least popular candidate, is eliminated. His or her votes are transferred based on next usable marked preference.
Perhaps the transfer will put one or the other over quota.
anyways, with E gone, only two candidates -- B and D -- remain for the one remaining open seat. Whoever is ahead after E's votes are transferred will take the seat.
The transfers of E's votes will help determine which of B and D will win the final seat.
If all of E's supporters bear no marked preference, B will win, having one more vote than E.
But if more are marked for D than B, then D will have more vots in the next stage, will be seen to be more popular and will take the seat.
On other hand, if more transfers are marked for B than D, then B will be seen to be more popular and will take the seat.
(This is brutal but like all elections, even under STV someone must win and someone must lose.)
At this stage, E's 51 votes are made up of these types:
38 marked E first preference and now we look at the second preference
10 marked A first preference and E as second preference and now we look at the next usable preference (likely 3rd but possibly the 4th, if C is marekd as 3 choice.
3 either marked C first preference and E as second preference
or they might be marked A first preference and C as second preference and E as 3rd preference. Now we look at the next usable preference (3rd or 4th).
Of the last 13 listed, when they were selected at random in earlier transfer from A to C, or C to E, or A to C to E, there was no reference made to the 3rd or 4th preference marked on the ballot. But now those later preferences have an impact on whether B or D will be elected.
The transfer of E's votes will help put B or D over quota or it will help set who is most popular in the next stage,
and thus who will be elected to fill the last seat - the least-popular candidate will be eliminated, leaving just one remaining candidate in the running to take the last seat - even if that person does not have quota. This is an artificial case in that usually candidates are more than one vote apart so not so much depends on random choices made earlier. And note that there was no certainty that the count would go to 4th Stage - on the second count the transfer of A surplus might have put two candidates over the quota, filling the last two remaining empty seats, and ending the vote counting process right there. There would not have been a transfer based on third preferences. so any dis-proportional of third preferences in the transfer would not have any effect. But this STV, despite the random flaw, does see most of the votes actually used to elect someone, someone preferred over others. 257-plus Effective votes of 358 cast Note that the filling of the first two seats has meant that 210 of the 358 total voters saw their first choice elected, and 40 of them have seen their first and second choice elected, and by the end a further 47-62 will see their first choice elected as well. In addition, some of E's first-preference supporters will see their second choice elected if they are marked for whichever of B or D wins in the end. At least 257 of the 358 voters see their first choice or second choice or both elected, and the number of votes used to elect first and/or second preference could go as high as 310 out of 358 votes cast, even with initial votes exactly as noted. Likely A and B were of different parties and perhaps A and C were of same party, so the A-C party had about 210 first choice votes (and did not take all the seats) while the B-E party had just 100 votes and has good chance of taking one seat. (party labels are intentionally not noted in this example.) This is a much more fair result than we see in FPTP or Block Voting, even with the random-effect of the whole vote system. We see too if the 60-vote surplus of A was transferred differently visa vis the 3d preference, then E might have passed D to not be eliminated. With enough support from back-up preferences on votes initially placed on others, E might have even won a seat. and this would have been reflective of how votes were cast and how back-up preferences were marked. The random selection of A's surplus transfer means the diversion from true proportionality may be just minimal. (In this case we never actually know the proportion of A's votes visa vis third preferences. (We only know what the second preferences were. This is true to real-life). Exact fractional transfers might have produced exactly the same transfers as the whole vote "random method" did here. We just don't know.
And we can see that A and C were elected, and one of either B or D, so all or most of the candidates in the winning positions in the first count went on to be elected. This is the usual outcome in STV elections - the transfers make little or no difference to the placing of candidates in the winning positions in the first count.
so even super-precise transfer methods make little difference - in this example only twice were surplus votes transferred - and those transfers involved just 71 of the 358 votes cast.
=========
For interest sake, here is an earlier version of the sample election.
The quota does not coincide with the total number of votes, which can happen at a later stage in the vote counting.
In this pretend election three are to be elected; there are five candidates
1 stage 2 stage 3 stage A 150 90 elected B 70 70 + 3 73 C 64 104 90 elected D 58 68 +8 76 elected E 55 65 +3 68 Votes for candidate A (elected) are: 100 A/C 25 A/D 25 A/E Quota is 90 surplus is 60 C gets 40 votes from A D gets 10 votes from A E gets 10 vote from A Stage 3 surplus of C is transferred when A surplus was transferred, later preferences were not considered but now the third preference on those are considered. they are now seen to be (just looking at next usable preference, ignoring any marked A) overall proportions of C's votes 3rd preference converted to the 14 surplus B 10 10 20 2.7 whole vote 3 D 34 24 58 7.8 whole vote 8 E 20 6 26 3.5 whole vote 3 total 64 40 104
This 14-vote transfer is put in the vote count table above we see that D is elected. But if the 60-vote surplus of A was transferred differently vis the 3d preference, then E might have passed D to win a seat.
But the random selection of A's surplus transfer means diversion from true proportionality may be just minimal. (In this case we never actually know the proportion of A's votes visa vis third preferences. This is true to real-life).
Conversely if D (or E) received enough votes in the transfer of A's surplus to make quota, there would not have been a 3rd stage - there would not have been a transfer based on third preferences. so any dis-proportional of third preferences in the transfer would not have any effect. ===================
see another Montopedia blog on the WGIM - the Weighted Inclusive Gregory Method of transfer of surplus votes, an example of super-precise method transfer, which actually has little impact on the course of the vote count.
===============================
Comments