Re: Unusual behaviour regarding default options and supermajority requirements.

```On Mon, Nov 18, 2002 at 12:31:42AM +1100, Clinton wrote:
> Assume a set of votes as below.
> CBA
> CBA
> CBA
> ACB
> BAC
> Not only has the condorcet winner lost, but this system has a distrubing
> property if the election is recounted, with the same set of votes, there
> is a new winner.
>
> Since B won, we'll make B the default option and give it supermajority
> protection of 2:1 vs all other options.

This isn't an entirely meaningful way of talking about things: eg, a
"none of the above" vote in a DPL election isn't the same as a "two
terms for Bdale" vote.

But still. If your first vote was:

A -- remove non-free
D -- further discussion

30 A B D
10 D A B
10 B D A

leading to an outcome of "B", you could legitimately expect another vote of
the form:

A -- remove non-free
D -- further discussion

30 A D
10 D A

with 10 other votes. I'm not sure I'm willing to agree that the people who
said that "removing non-free, or even handwaving about it is dangerous
-- we need to discuss it more before we even think about doing it" are
going to say "well, we've handwaved about it, might as well actually do
it". If they're not, then the result is stable: 30 A D votes to 20 D A

Stability isn't necessarily achievable though. It might be a similar
problem to the "A defeats B, B defeats C, C defeats A" issue: as soon
as you choose A as the winner, you can have another vote with just C as
an option, rinse, and repeat.

One way of achieving stability is to make the default option win more often.

30 A B D
10 D A B
10 B D A

can be treated as:

D beats A: 20:15 (scaled)
A beats B: 40:10
B beats D: 40:10

then, rather than eliminating anything, calculate the Schwartz set as
{A,B,D}, note the default option is a member of the Schwartz set, and
declare it the winner.

An alternative is to let people express their preference for the current
way of doing things without having to invoke the superpowers of the default
option. Thus:

A - remove non-free
L - leave things as they are
D - further discussion

lets our voters say:

30 A B L D   (A B D)
10 L A B D   (D A B)
10 B L D A   (B D A)

with the result that:

A beats B: 40:10
A beats L: 30:20
A beats D: 40:10 (scaled: 20:10)
B beats L: 40:10
B beats D: 50:0
L beats D: 50:0

and A wins, stably. In general, you should probably treat putting
something below the default option as meaning you don't think this is
ready to be considered, not simply that you prefer what we're currently
doing.

> In my opinion, having repeated elections with identical votes produce
> different results and requiring repeated elections to get sencical
> results [...]

It's actually an efficiency bug at worst, as far as has been demonstrated.
Which is lame, but not horribly bad.

Cheers,
aj

--
Anthony Towns <aj@humbug.org.au> <http://azure.humbug.org.au/~aj/>
I don't speak for anyone save myself. GPG signed mail preferred.

``If you don't do it now, you'll be one year older when you do.''
```

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