[EM] SODA

[fsimmons at pcc.edu]

Jameson suggested that the SODA candidates make their approval decisions sequentially instead of 
simultaneously.

The problem with this is that if a winning candidate moves to first place in the sequence by an increase 
in support, she may become a losing candidate:

Assume sincere preferences are

35 A>B>C
34 B>C>A
31 C>A>B

If approval decisions are made in descending order of faction size A, B, C, then B wins.

If B gains more support so that the totals become

34 A>B>C
35 B>C>A
31 C>A>B,

the sequential order becomes B, A, C, and the winner will be C.

Going from smallest to largest has its problems, too.  I don't think it fixes the monotonicity problem, and 
it introduces other problems like changing what would be the game of chicken in the simultaneous case 
into a clear cut win for the smaller faction:

49 C
27 A>B
24 B>A

In the simultaneous case there is a game of chicken between A and B.

In the sequential case whichever member of the set {A,B} goes first wins.

How can we fix this?

How about allowing the largest faction (in this example 49 C) to go second, and making the second 
largest faction (in this example 27 A>B) go first?

That would also work in the example above.  How bad would it be in a worst case example?