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Investopedia explains 'Arrow's Impossibility Theorem'
For example, the following shows the type of problem typical of an election. Consider the following example, where voters are asked to rank their preference of candidates A, B and C:
• 45 votes A > B > C (45 people prefer A over B and prefer B over C)
• 40 votes B > C > A (40 people prefer B over C and prefer C over A)
• 30 votes C > A > B (30 people prefer C over A and prefer A over B)
Candidate A has the most votes, so he/she would be the winner. However, if B was not running, C would be the winner, as more people prefer C over A. (A would have 45 votes and C would have 70). This result is a demonstration of Arrow's theorem.
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