other devious electorate solutions
Blake Cretney
bcretney at my-dejanews.com
Tue Nov 10 16:34:45 PST 1998
It occurs to me that one of the simplest cures for strategy problems
is also a natural result of devious electorates. That is lying to
pollsters.
For example
40 A B C
13 B A C
12 B C A
35 C B A
Sincere votes
A B C
A X 40 53
B 60 X 65
C 47 35 X
So, by LCM (my method)
A > C 53-47
B > C 65-35
B > A 60-40
So, B wins, as every other candidate is one-way beat path defeated.
What if A tries a little order-reversal strategy?
40 A C B -- sincere A B C
13 B A C
12 B C A
35 C B A
A B C
A X 40 53
B 60 X 65
C 47 35 X
A > C 53-47 = 6
C > B 65-35 = 30
B > A 60-40 = 20
No one has a one-way beat path to it, so the least majority (A>C)
is dropped. Leaving C>B and B>A. So, C wins.
But A would know not to do this because of the polls, right?
But what if a large number of C voters told the pollsters they
were actually A supporters.
Lies
40 A B C
5 A B C - these voters are lying, they are actually C supporters
13 B A C
12 B C A
30 C B A
This might cause the A voters to try order-reversal because of
45 A C B
13 B A C
12 B C A
30 C B A
A B C
A X 45 58
B 55 X 25
C 42 75 X
A > C 58-42 = 16
C > B 75-25 = 50
B > A 55-45 = 10
B>A dropped resulting in win for A.
However, the actual result if A falls into the trap is a victory
for C, as demonstrated in the first order-reversal example.
---
Blake
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