[EM] Approval vs. IRV

[Gervase Lam]

> Date: Tue, 12 Oct 2004 20:34:41 -0700
> From: James Cooper
> Subject: [EM] Approval vs. IRV

> The requirement to rank all the
> candidates also results in some odd side effects (like 'how to vote'
> cards, and the horrific 'donkey vote').

May be it is not strictly a 'how to vote' card, but for Approval, I think 
there should be some instructions/guidelines so that voters know who to 
vote for.  Otherwise, I think the voters will vote unwisely (e.g. bullet 
voting when they shouldn't, voting for too many candidates, etc...)

For example, in the zero-info case (i.e. there is no poll information, the 
election is basically wide open to every candidate), the guideline could 
be something on the lines of:

"Vote for the candidates who you think are above average (the average of 
all the candidates)."

However...  I will go into a little diversion...

I was recently watching a sort of TV documentary that involved 
psychologists being able to predict what people were going to do in 
certain "everyday" situations.  They did this by using the Gregg-Meyerson 
test.

The test, involved answering several multiple choice questions.  Viewers 
could also particpate as the questions were shown on the screen.  For 
example, one of the questions was:

"You are going to the supermarket to stock up on food.  How would you work 
out what to buy?

1. List every item to be bought, in aisle order.
2. List the items to be bought.
3. Make a rough list of items to be bought.
4. Just get there and wander around, taking whatever you fancy."

After answering the questions, you were then told that if you mostly chose 
1s or 2s, then you are a planner.  If you mostly choose 3s or 4s, then you 
are spontaneous.

However, isn't it more accurate to say, that the lower the average, the 
more of a planner you are.  The higher the average, the more spontaneous 
you are.

The reason the documentary makers did this was obviously because they 
wanted to keep things extremely simple.  Now, if things should be this 
simple, then calculating the "average of all the candidates" isn't on.

The only other thing I could think as an appropriate guideline for the 
voters to use the median average instead of the mean average utility 
to work out who to vote for.  After all, most of the time, the median is 
about the same as the mean average.  So this changes the voter guideline 
to:

"Vote for the top 50% of the candidates."

But what if the voting population think that candidates are extremely 
polarised?  For example, a voter may think that 33% of the candidates are 
very near the 10 out of 10 mark, while the remaining candidates are very 
near the 0 out of 10 mark.  This would mean that the median is near the 0 
mark.  Therefore, according to the guidelines, the voter would vote for 
candidates who gets almost 0 out of 10 marks.

One could hope that there would be enough voters who have the median at a 
more sensible place.  However, factionalism (group/mass psychology) could 
be involved.  Therefore, the whole voting population could have 
polarised views.

One way around this polarisation problem is to add extra guidelines like, 
"but if you feel the candidates are very good or very bad, with nothing in 
between, then just vote for the very good candidates."  Even adding this 
extra guideline can't cope with more intricate distributions of utilities.

Also, more guidelines are needed for non-zero-info situations.  In other 
words, there must be some polling information around.

How reliable is the poll?  For example, practically all of the polls in 
the 1992 UK elections got things wrong.

Voters might as well be told just to rank the candidates.  That's all of 
the instructions that the voter needs to vote using a ranked ballot.  No 
other guidelines are required.

Ranking is the next best thing, with the downside being that there is the 
loss of utility information in a rank ballot.  But, by voting for the top 
50% of the candidates in Approval, the utility information is lost anyway.

All of this has made me swing back to Condorcet.  My future needs, which 
are non-political, are simple.  This is why I have currently sided on 
using Plain Condorcet (Max Opposition).  I would probably explain it 
something like the following:

"A ranked ballot...

1st. A
2nd. B
3rd. C
4th. D

...contains a lot of information.  If a voter submitted such a ballot, it 
shows that the voter has ranked A over B, A over C, A over D, B over C, 
etc...  All of these individual head-to-heads can be added up.

Let's take the following example.

42 voters ranked 1st:A 2nd:B 3rd:C 4th:D
26 voters ranked 1st:B 2nd:C 3rd:D 4th:A
15 voters ranked 1st:C 2nd:D 3rd:B 4th:A
17 voters ranked 1st:D 2nd:C 3rd:B 4th:A

This can be summarised in the following table:

B 42:A 32:C 32:D
A 58:B 58:C 58:D
C 68:B 42:A 17:D
D 83:C 68:B 42:A

In the first line of the table, labelled candidate B, the "42:A" means 
that 42 voters ranked A over B, the "32:C" means that 32 voters ranked C 
over B.  In the second line of the table, labelled candidate A, the "58:B" 
means that 58 voters ranked B over A.

Note that within each line, the numbers have been sorted in descending 
order.

The winner is the candidate whose left most number is the least."

The documentary also got me thinking about another thing.  The 
psychologists divided some people who had gone through the Gregg-Meyerson 
test into two groups.

Each group were about to go on a helicopter ride.  However, one person 
from each group had to be left out.

One group tried to choose the person who should be left out by working out 
what who was most physically suited to go into the helicopter.  I think 
they eventually decided to put it to a vote.

Meanwhile the other group had a very hard time deciding who should be left 
out.  Their view was that everybody in their group should go into the 
helicopter and that it was not at all fair that somebody had to be left 
out.  They even tried to persuade the "referee" to let everybody go on!

This latter group made me think about Condorcet.  With Condorcet, you 
should rank everybody fully, however marginal the difference is between 
two candidates.

For example, in a 100m race, if I were running against a world class 
runner, I would probably be 60m behind when the first person crossed the 
finish line.  However, if there was also a second world class runner, even 
though was a 1/4 inch behind when the other runner crossed the finish 
line, the three runners would still be distinctly ranked.  There would be 
no tied rankings.

Considering this, should rankings like "A>B=C=D" be considered to be 
"A>B?C?D"?  In other words, there would be no tied rankings, only "?" 
because a voter could not decide between the candidates, a bit like the 
group who could not decide who should not go on the helicopter.

OK, this can be more sophisticated.  But I want to keep to "transitive" 
ballots for the time being.

Thanks,
Gervase.