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"