[EM] Randomized MCA, new weird voting method idea

[Chris Benham]

Warren Smith wrote:

>I'll describe a new voting method.  I'm not sure if it is brilliant
>or crazy.  I'm also unsure how to analyse it.
>
>1. Forest Simmons has often advanced the idea of using randomness in voting
>methods inspire more voter honesty. ("Lottery methods.")
>
>2. IEVS (my simulator - see http://groups.yahoo.com/group/RangeVoting
>if you want news about what IEVS is finding out)
>says MCA is one of the best methods.
>
>3. So here is a new idea intended to take advantage of both ideas.
>It is a different-than-usual way to use randomness.
>
>Consider the following randomized variant of the "MCA" voting method.
>Voters rate each candidate either 1, 2, or 3 (3 is best).
>The candidate with the most 3-ratings wins if his number of
>3-ratings exceeds X% of the number of voters.
>Otherwise, the candidate with the most {2- or 3-ratings} wins.
>
>Here X is chosen randomly and is not known to the voters when casting
>their votes.
>
>The point is: if X were some fixed known constant (conventional MCA
>method: X=50%), then with a huge number of voters,
>it would be virtually certain the election would end in the 1st round,
>or virtually certain it would end in the 2nd round. The voters
>would get wise to which. Once they knew which round it was going to be,
>then the election would really just be an approval-voting election,
>and any advantages of the 3-slot over regular 2-slot voting, would
>essentially not exist.  
>  
>

I think the difference between "virtually certain" and *guaranteed* can be 
important/significant. Election methods in my book shouldn't be assumed to be
of equal merit just because they nearly always (in simulations and/or in 
practice) elect the same winner. 


Limiting voters to expressing two preference-levels is in my book 
unacceptable and three is a big
improvement. Warren, do you prefer "Range3" to Approval?

When the voters are informed strategists and/or if they are mainly 
concerned that the winner come
from a certain subset of candidates, then all FBC methods have at least 
a very strong tendency to
become equivalent to Approval.

To comment on the specific method proposal: it looks crazy to me. The 
method no longer meets
"3-slot Majority for Solid Coalitions":

35: A
33: B>C
32: C>B



If  X is revealed as 35% or lower, then A wins in the first round.

Or  "3-slot Condorcet(Gross)":

26: A>B
25: B
25: C>B
24: D>B

If  X is revealed as 26% or lower, then A wins in the first round.


A faction that believes their favourite is the FPP winner might have 
extra incentive to only put that
candidate in the top slot, but apart from that the main effect of the 
change is that voters will have a
greater fear that their Worse will win in the first round so their 
incentive to ignore the middle slot
will be increased, making the method (even) more like Approval, not less.

Chris Benham