PR system - can it be inconsistent?

tails_naf

I have been reading up on the Proportional Representation election system we have, and it seems to boil down to -

- a quota is set, say 50 votes.
- once a candidate is elected, any surplus votes he has are redistributed to all candidates and the 2nd preference is used
- if no one is elected, the bottom candidate is eliminated, and his 2nd preference votes are re-distributed.

- repeats for 3rd, 4th, and subsequent preferences.

This all sounds good, and fair - but I was wondering if the following could happen

Say we have candidates A B and C (plus D, E, F..etc)
Quota is 50.
A has 60 votes, B and C have 48 each.

the 10 surplus from A is redistributed, and say the break down is 1 to B and 3 to C
So now C gets elected.

However, this depends on WHICH 10 votes are marked surplus.
In a very close race, I imagine which 10 are chosen could make a difference.

So is there truth in this - if there was a recount (and the count is accurate) depending on which votes are marked surplus and which are not, could change from count to count...and so could the person who would be elected B or C. So how would such a deadlock be broken?

RGDATA!

tails_naf wrote: »

I have been reading up on the Proportional Representation election system we have, and it seems to boil down to -

- a quota is set, say 50 votes.
- once a candidate is elected, any surplus votes he has are redistributed to all candidates and the 2nd preference is used
- if no one is elected, the bottom candidate is eliminated, and his 2nd preference votes are re-distributed.

- repeats for 3rd, 4th, and subsequent preferences.

This all sounds good, and fair - but I was wondering if the following could happen

Say we have candidates A B and C (plus D, E, F..etc)
Quota is 50.
A has 60 votes, B and C have 48 each.

the 10 surplus from A is redistributed, and say the break down is 1 to B and 3 to C
So now C gets elected.

However, this depends on WHICH 10 votes are marked surplus.
In a very close race, I imagine which 10 are chosen could make a difference.

So is there truth in this - if there was a recount (and the count is accurate) depending on which votes are marked surplus and which are not, could change from count to count...and so could the person who would be elected B or C. So how would such a deadlock be broken?

i don't know the exact mechanics of this but my understanding is the surpluses are calculated proportionally.
i.e. if it was as close as in your hypothetical example all the votes would be counted and the transfers calculated based on the ratio of all the votes.
if that makes sense.

edit:

Sad Professors answer (below) is better

Sad Professor

tails_naf wrote: »

However, this depends on WHICH 10 votes are marked surplus.
In a very close race, I imagine which 10 are chosen could make a difference.

Yep, in the case of a surplus, a "random sampling" of ballots is actually transferred to the next candidate. This doesn't affect the second preference candidate who gets the same number of votes no matter what, but it means any future transfers (3rd preference, etc) aren't counted properly. So, yes, a re-count could come up with a different result based on which particular ballots get transferred.

As I said on another thread, ideally in the case of a surplus they should transfers ALL votes at a fraction of their value. So if the candidate has a 50 percent surplus, all of his votes would be transferred to the second preference candidate at the value 0.5. This would get very complicated after a few counts though. This is what is done in senate elections, but it is considered too costly and time consuming for general elections.

It should be noted this isn't a PR problem, or even an STV problem, just a problem with the way we count votes.

dilallio

Here's a post from boards user Upmeath yesterday which has an excellent link to how it all works. Well worth going through the podcast'

http://www.boards.ie/vbulletin/showpost.php?p=70747176&postcount=8

drkpower

I (hope I) get all of the mathematical issues over the distribution of a surplus. But here is a quick Q.

Lets say, the quota is 8000, and Candidate A has a 10000 votes, and a surplus of 2000. So then the number 2s of all 10000 votes are analysed in order to come up with the appropriate percentage of the 2000 surplus that should be transferred to Candidates B,C & D. So, if Candidate B is no. 2 on 5000 of Candidate As votes, Candidate B will get half of the surplus, namely 1000.

But what physical papers get transferred to B? Is it simply a matter of randomly shuffling the 5000 papers Candidate B is no. 2 on and picking 1000 of them to physically transfer onto his pile?

Many thanks (im going to lie down now...)

Sad Professor

drkpower wrote: »

But what physical papers get transferred to B? Is it simply a matter of randomly shuffling the 5000 papers Candidate B is no. 2 on and picking 1000 of them to physically transfer onto his pile?

Yes, as said above, it's a random sampling.

drkpower

Sad Professor wrote: »

Yes, as said above, it's a random sampling.

`Thanks Prof.

In your post above, you said a re-count could come up with a different result based on which particular ballots get transferred.

So are you saying that a re-count actually results in an entirely new bunch of papers being physically distributed on to Candidate B's pile?

I always thought that a recount just meant that the votes were literally recounted in the way they were initially redistributed, rather than an entirely new redistribution occurring.

Sad Professor

Well, I meant if everything was recounted from scratch.