[EM] PLEASE consider: More non-deterministic methods

[wclark at xoom.org]

Jobst Heitzig wrote:

> Although there has been only one reply to my previous posting on
> non-deterministic methods, I still consider it more and more important
> to study such methods.

> They seem to be *the only chance* to avoid incentives to produce fake
> Condorcet winners by strategic voting!

Not only that, but they're the only chance to get consistent substantive
fairness in certain situations.  Random ballot, for instance, can be
thought of as the probabilistic time-sharing equivalent of PR for a
multi-member body.

If Greens make up 3% of the vote, year after year, then roughly 3% of the
time we should have a Green president.  Or, equivalently over the long
term, we should have a 3% chance of electing a Green president in any
given election.  So say proponents of substantive fairness (fairness in
results), at least.

Deterministic methods supply (nearly perfect?) *procedural* fairness, but
hardly any *substantive* fairness at all (these distinctions are discussed
at length in various works by Lani Guinier:
http://en.wikipedia.org/wiki/Lani_Guinier ).  Any reasonable deterministic
method will always select the majority winner -- even though substantive
fairness might require a minority candidate to win occasionally.

One major problem with non-deterministic methods is, well, the fact that
they're non-deterministic.  That means you have to trust whoever is in
charge of declaring a winner (or providing your source of randomness). 
Non-deterministic methods are generally very highly deficient in
procedural fairness, even though they often produce fair outcomes in the
long run (assuming they're not corrupted).

So basically, non-deterministic methods are the exact opposite of
deterministic methods.  Just like you'd expect.

But I think you're right in saying that this area needs more research. 
For instance, hybrid methods that are deterministic under certain
conditions (such as when there's a majority winner) and non-deterministic
at other times may end up striking a better balance between procedural and
substantive fairness than non-hybrid methods alone.

You could even use non-deterministic procedures to "blend" different
methods together:  When both methods agree on a winner, use either IRV or
Condorcet.  When they disagree, use either method with likelihood
proportional to the number of voters ranking its winner as their first
choice.  (Or something similar.)

Non-deterministic methods look like they could be a lot of fun.

-Bill Clark

-- 
Protest the 2-Party Duopoly:
http://vote.3rd.party.xoom.org/