Tuesday 18 January 2011

Ignorance vs Lies

My (completely unrelated to any bias the system gives to support one party over another i.e.) mathematical problem with AV.

If we take on board that different preferences differ in amount of support they symbolise (which is the definition of a preference after all) and we accept that averaged out people’s first preferences have more support that second, we can make inroads to putting a value against the preference.

I started out on the assumption of values that showed that first preference is 1, second preference is .5, third preference .25, fourth preference .125 but after much talk with various people was convinced that people do often favour their choices a lot closer.

For this reason I have revised my example to 1, 0.75, 0.50, 0.25

This area can be studied and is in other fields like pain research where the collective subjective value is averaged out to approximate an objective value.

So say we have three parties running

A B C

A has 12 votes, B has 9 votes, C has 8 Votes.

This under FPTP would produce a win for A.
Arguments against this would be that 17 people DIDN’T vote for them. This is a valid argument.
Arguments for this is that given what we know, out of A, B and C,
A has most support. This is a valid argument too.

Now lets try under AV

A has 12 votes, B has 9 votes, C has 8 Votes.
C is eliminated. Let’s say the votes are split 6 to B and 2 to A.

Votes now read
A has 14 votes (12 first preference and 2 second preference)
B has 15 votes (9 first preference and 6 second preference)

Under AV, B wins.

Argument for this is that it allows some of those eliminated to still be involved.
Argument against this is that not every voter was as involved as the next.

Now, lets apply value of vote

A has 12 first preferences and 2 second preference, meaning a total support value of 13.50

B has 9 first preferences and 6 second preferences, meaning a total support value of 13.50
So in affect we have a draw.
Please bare in mind this is with a generous weighting as it is (that you might support your second preference candidate only 25% less than your first).

So AV has given us a false result.
The margin of error will only increase more and more when smaller preferences weighted at 0.5 and 0.25 are introduced into the mix.

That is the first mathematical problem under AV, but stick around because the level of potential error is going to get a lot bigger.


Let’s go back to our previous example to keep things fair.

A has 12 votes, B has 9 votes, C has 8 votes. Under AV we asked for the preferences and since AV does not publish them all, lets do that now

A has 12 votes, they second preference C (they are dead against B, their main rivals)
B has 9 Votes, they second preference C (they are dead against A, their main rivals)
C has 8 Votes, they second preference 6 to C and 2 to A (no real rivalry, just a leaning to B)

(Can you see who it is yet?)

Now we have a much better understanding of the will of the people, don’t we.
Why would any system not tell us this?
Why take all that useful data and class more than half of it as irrelevant?

Now let’s use the value weighting.
A has 13.5 as before
B has 13.5 as before
C has 23.75

If we changed the weighting to 1, .5, .25, etc
The result would be
A has 13.5
B has 12
C has 18.5

Say we took it ridiculous and changed weighting to 1, .25, .01
The result would be
A has 12.5
B has 10.5
C has 13.25

Even taken to that degree, it is quite clear that B should NEVER win.
It didn’t have the most first preferences, and it didn’t have the most second preferences. (Adding logical 1st prefs would only help A as only C are likely to 'third preference'. A are likely to get 6 third prefs and B only 2 third prefs but that isn't even needed to show my point).

The weighting value which I conceded to of 1, .75, .5 makes it more obvious. Under my previous 1, .5, .25 it is closer but still obvious who should win.

That is just one anomaly. What if the people from A didn’t mind B? Or vice versa? You could have a different result again to the AV result. In fact the mind boggles at how much data is ignored by AV.

For this (mathematical) reason, it is clear to conclude that by counting only the smallest parties vote, you are getting an incorrect picture of total support.

FPTP, even though not ideal and less sophisticated has at least one thing going for it that AV doesn’t. You can only win if you have the most votes according to ALL it's data.

The difference in a sound bite would be
"FPTP can be ignorant, but AV can Lie"

10 comments:

  1. Oh deary me. Strawman right here, and from someone said to loathe them.

    For a start, how can you even start to talk about weighting people's votes? They have one vote and that gets transfered. It's binary, it is on or it is off...it is an endorsement, a supporting statement, or it is not present, and a statement of lack of support.

    If someone under AV puts preferences for 3 out of 5 candidates it's because they would be happy to be represented by 3 out of 5 candidates. Weighting doesn't come in to it.

    HOWEVER. Let's look at your example again, given you like the idea of weighting. I'll make my own kind of strawman to counter your "maths".

    Your FPTP results... "A has 12 votes, B has 9 votes, C has 8 Votes."

    Let's say that of those voting A they have an average "support value", how much they care about that candidate getting in specifically, of 0.62. B has an average support value of 0.75, but C has a support value of 0.95. Applying this weighting, which is entirely as prevalent (but equally as irrelevant) as under AV, we have the following results.

    A has a 7.44 vote share
    B has a 6.75 vote share
    C has a 7.6 vote share

    Oh look! C is actually the winner!

    Except, of course, electoral systems are not about how much you care, only if you care enough to give your candidate your preference (however many that may be allowed) your endorsement or not.

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  2. Oh, and to just put the cherry on the cake of this. FPTP is also a lie in the following scenario.

    9 people vote A because they love A,
    6 people vote B because they love B,
    3 people vote A because they'd rather have C but fear B getting in.
    3 people vote B because they'd rather have C, but fear A getting in.
    8 people vote C, because they love C.

    C, in total, under FPTP here, has 14 "loves", while A and B only have 9 and 6 respectively. Yet due to some tactical voting C has actually come last, rather than first.

    So perhaps your final line should be "FPTP can be ignorant, and a lie, but at least AV can only be a lie...and only in such a way that the minority party in 1st preference ballots doesn't get the power as FPTP advocates fear."

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  3. You have misunderstood the point of this post. I haven't given different weighting value for each party, that would be ridiculous (and is the only straw man argument on this page) I have done it by preference. In short my weighting suggests that a labour activist supports labour in the same way a tory activist supports the conservatives. Yours example claims supports of one party do it more so then other people support their own.

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  4. OK, now that I am on my PC I can dissect a bit more.

    1)I can talk about weighting peoples votes because they are weighted in real life. Someones 1st preference is prefered to their second...it is worth more and weighs more.

    2) If someone under AV puts preferences for 3 out of 5 candidates it's because they would be happy to be represented by 3 out of 5 candidates. ....wow, so you DON'T think someone prefers their 1st preference to their 3rd?

    3)I have dealt with the differen weightings for different parties strawman argument of yours about (again different preferences indicate level of support not different political views)

    4)The FPTP lying thing. So in your example, 6 people tell the vote counters something that isnt true and this means the voting system is a liar? Not the voters?

    4b) You seem to have a habit of making examples of voting patterns while including information that would never be known. Like in your AV example where you used the 2nd places preferences (which are irrelevant under AV) to prove your point. Here you are using "They would rather..BUT" That is not an option under fptp.
    All the voting system deals with in your example is
    12 people vote A
    9 people vote B
    8 people vote C
    (if the voters were more honest the results would read)
    9 people vote A
    6 people vote B
    14 people vote C
    SO if everyone had voted for who they wanted to win (like FPTP is designed to do), the right party would have won.
    (Nothing to fear if your honest)
    If I told you a lie, and you not knowing it is a lie, tell someone else, does that make YOU a liar? I don't think so. It would make you ignorant.
    If I told you the truth but you cherry picked parts of what I said, and therefore using flawed information said a lie, THAT makes you a liar.

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  5. Before you two go any further with this, I absolute must highlight that bringing in weighting of preferences would give voters an incentive to vote tactically, something that AV is pretty good at avoiding. If higher preferences have more value the temptation would be to give them to the parties with more chance of keeping out the disliked one. First past the post is effectively an extremely weighted preference system, giving 100% weighting to what you declare as your first preference and zero weighting to all of your other preferences. Although DBirkin's proposed weighting method is far more moderate it would still lead to tactical voting.

    Weighted preferences are unnecessary anyway. The point of AV is to give your vote to the highest placed candidate in each round.

    Nor is it necessary to count everyone's preferences because we have a system of one person one vote. If your vote goes to your highest placed candidate then it would be unfair to demand it go to another candidate as well and it would certainly be against the voter's wishes to transfer a vote from a candidate who has a chance of winning to a less preferred one.

    Furthermore if you had weighted preferences you would have to make ranking of all candidates compulsory. Not everyone has relative preferences of every candidate worked out, if it were mandatory to fill the ballot with a full list you'd end up with a lot of random choices, or donkey votes as they're known. This would be just as bad as tactical voting because you'd end up with a lot of untrue information bringing down the signal to noise ratio.

    So what if to get around this you made it possible to put multiple prefs for the same candidate, but having to include as many preferences as there are canddiates? Well this would make everyone's vote count the same and get around donkey voting, yes. But it would degenerate into the extreme tactic of ranking every preference with a single candidate. You'd be right back where you started, with First Past the Post.

    Given that the criticisms of AV here apply ten fold to FPTP you can infer form this that AV is the best option currently available. I'd love Condorcet, but I don't imagine it would ever be offered, and its complexity could well stop people from voting for it. And in light of that I'll happily take AV instead. It's not a bad second choice to Condorcet at all.

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  6. Before you two go any further with this, I absolute must highlight that bringing in weighting of preferences would give voters an incentive to vote tactically, something that AV is pretty good at avoiding. If higher preferences have more value the temptation would be to give them to the parties with more chance of keeping out the disliked one. First past the post is effectively an extremely weighted preference system, giving 100% weighting to what you declare as your first preference and zero weighting to all of your other preferences. Although DBirkin's proposed weighting method is far more moderate it would still lead to tactical voting.

    Weighted preferences are unnecessary anyway. The point of AV is to give your vote to the highest placed candidate in each round.

    Nor is it necessary to count everyone's preferences because we have a system of one person one vote. If your vote goes to your highest placed candidate then it would be unfair to demand it go to another candidate as well and it would certainly be against the voter's wishes to transfer a vote from a candidate who has a chance of winning to a less preferred one.

    Furthermore if you had weighted preferences you would have to make ranking of all candidates compulsory. Not everyone has relative preferences of every candidate worked out, if it were mandatory to fill the ballot with a full list you'd end up with a lot of random choices, or donkey votes as they're known. This would be just as bad as tactical voting because you'd end up with a lot of untrue information bringing down the signal to noise ratio.

    So what if to get around this you made it possible to put multiple prefs for the same candidate, but having to include as many preferences as there are canddiates? Well this would make everyone's vote count the same and get around donkey voting, yes. But it would degenerate into the extreme tactic of ranking every preference with a single candidate. You'd be right back where you started, with First Past the Post.

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  7. This comment has been removed by the author.

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  8. I don't understand. You just appear to be making up numbers.

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  9. James, I know the math will go over some people's heads. The basic principlke is that the mechanics of the count under AV does little to find the most supported out of the candidates.

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