Arrow Paradox

Arrow Paradox
Preferences in HP, Color, and Sex Appeal

	Horse Power	Color	Sex Appeal
Chevy	PREFERRED
Ford		PREFERRED
BMW			PREFERRED

Preferred one to another

	1st Preference	2nd Preference	3rd Preference
HORSE POWER	Chevy	Ford	BMW
COLOR	Ford	BMW	Chevy
SEX APPEAL	BMW	Chevy	Ford

This idea is very simple given the data above. 


the data it indicate:
Chevy is preferred to Ford 2:1
Ford is preferred to BMW   2:1
BMW is preferred to Chevy  2:1
-or-
BMW is preferred to Chevy which is preferred to Ford which is preferred to BMW which is preferred to Chevy which is preferred to Ford.. etc...


Unless there is a different weight for each preference, you can not make a choice between Ford, BMW, and Chevy.


This argument is used to say that there is no democracy. All democracy has to do with is the order in which candidate A vs. B vs. C approach each other (or the order in which you present Chevy vs. Ford, then Chevy vs BMW).


"it has been said that you can rig an election by presenting alternatives in a specific order."


Using the example above:
If I present Ford vs. BMW as your first two alternatives, then you pick Ford because it is preferred 2:1 to BMW.
If I then present Ford vs. Chevy it is preferred to ford 2:1, therefore you pick Chevy. but if I had presented BMW the first time, you would have picked BMW.