other devious electorate solutions

[Blake Cretney]

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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