Agenda Manipulation and Chairman’s Paradox
One fine day Moe decided to seize
absolute power. To this end he rigged an election. His nefarious scheme
succeeded, but it didn’t do him any good.
“Boys,” he said after a
particularly confusing wrangle, “we’re getting too many tie votes. I say we
need a chairman to cast tie-breaking votes!”
“That’s a good idea!” Curly
enthused. “But who should be the chairman?”
“Who but me?” said Moe. “Wasn’t I
the one clever enough to think of the idea?”
“But I’m not so sure I want you
for Chairman,” Larry ventured.
“Why then, let’s put it to a
vote,” said Moe.
“That’s fair,” said Curly. “I
nominate myself!”
“And I nominate myself,” Larry
added.
After much bargaining,
discussion, and fisticuffs, they settled on these preferences:
Moe: Curly < Larry < Moe
Larry: Moe < Curly < Larry
Curly: Larry < Moe < Curly
Larry
<
< 2/3 majority each
Curly > Moe
“This isn’t getting us anywhere,”
Curly complained.
“Why not try a run-off election?”
Moe suggested.
“You’d be the last person
I’d vote for!” Larry said.
“Okay,” said Moe, “then why don’t
you and Curly face off?”
“That sounds fair,” said Curly;
and so the first round of voting was between Larry and Curly.
Larry won the first round, thanks
to Moe’s and Larry’s vote. But then Larry faced Moe, who won with Moe’s and
Curly’s votes:
Larry Curly
\ /
Larry Moe
\
/
Moe
Had Larry been the last one
considered, then the elections would have been like this:
Moe Curly
\ /
Curly
Larry
\
/
Larry
And had Curly been the last one
considered, then the elections would have been like this:
Larry Moe
\ /
Moe Curly
\
/
Curly
Therefore, in an election like
this, the last one to be considered wins. That’s Agenda Manipulation; how Moe become
Chairman of the Stooges!
“Well then!” Moe said, eagerly
rubbing his hands. “Let’s decide a few things, shall we? Eh, boys?” Larry and
Curly looked up. They had been discussing something together. Moe continued,
“Now let’s try ranking fairness, power, and logic. Which is best? Curly?”
“Fairness is best,” said Curly.
“How about you, Larry?” Moe said
gleefully. He was expecting an answer of ‘Logic’, so he could vote ‘Power’ and
invoke a tie.
But Larry said, “I agree with
Curly.”
More sophisticated voting! For
Larry was going along with his second-favorite choice, to keep Moe from
exercising the chairman’s power.
“Oh,” said Moe, crestfallen. “All
right then, which one is your least favorite? Larry?”
“Power is worst,” said Larry.
“How about you, Curly?” Moe was
expecting an answer of ‘Logic’, so that he could vote ‘Fairness’ and invoke a
tie.
But Curly said, “I agree with
Larry.”
Once again, a sophisticated vote!
Curly went along with Larry’s choice, to keep Moe from using the chairman’s
power.
Moe said grimly, “I see. And is
Logic in the middle?”
“That’s what you believe,”
Curly said.
“So that’s how we’ll vote,” Larry
added.
Actual preferences:
Moe: Fairness
< Logic < Power
Larry: Power < Fairness < Logic
Curly: Logic < Power < Fairness
Preferences according to
Sophisticated Vote:
Power < Logic < Fairness
“But that’s the exact opposite of
what I want!” Moe yelled.
“That’s because you’re chairman,”
Larry explained.
Curly added, “Now we have a reason
to gang up on you!”
“Power corrupts, and mathematical
power corrupts mathematically,” Larry explained.
“It’s the Peter Principle,” Curly
confided. “You’ve just risen to your Level of Incompetence!”
“That is what the troika is for,”
Larry explained.
Curly chirped, “It’s a king
trap!”
Moe hollered, “And I’m the Stooge
who fell for it!”
Curly chuckled:
nyuck-nyuck-nyuck!
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