For a voting system (ranking of some candidates based on preferences of voters), it would be nice if:
- A single voter cannot determine the ranking (as a dictator)
- For every possible set of voter preferences, there is an outcome (not random)
- If everyone likes candidate A over candidate B, then in the final ranking candidate A should be ranked higher than candidate B
- If one prefers A over B when comparing just A and B, then one should also prefer A over B when an additional option C is offered
Sounds like some reasonable properties for a voting system, right?
Well, the theorem states that if there are more than 2 candidates, then there is no voting system that has all 4 properties above.
For a voting system (ranking of some candidates based on preferences of voters), it would be nice if:
- A single voter cannot determine the ranking (as a dictator) - For every possible set of voter preferences, there is an outcome (not random) - If everyone likes candidate A over candidate B, then in the final ranking candidate A should be ranked higher than candidate B - If one prefers A over B when comparing just A and B, then one should also prefer A over B when an additional option C is offered
Sounds like some reasonable properties for a voting system, right?
Well, the theorem states that if there are more than 2 candidates, then there is no voting system that has all 4 properties above.