Veritasium: Why Democracy Is Mathematically Impossible?
While briefly going back to the topic of opinion dynamics let us become familiar with one possibly unsolvable real-life problem. In other words, did you know that democracy is mathematically impossible?
For a democratic decision making mechanism (e.g., elections) to work properly, we must ensure that:
- Choice rankings should be transitive. If choice A is preferred over choice B, and B is preferred over C, then A should be preferred over C.
- Some decision should always be made. The mechanism simply can't "give up" under any however unusual circumstance.
- There should be no dictators. The decision must not depend only on one voter's decision.
- The mechanism should be unbiased, it should not impose any preference on the voters. If voters prefer choice A over choice B, this should be taken into account.
- Voter preference between two alternatives should depend only on the two alternatives. For example, if a group of voter prefers choice A over choice B, then introduction choice C should not change the relative ranking of A and B.
Seems reasonable, but it is impossible as per the Arrow's impossibility theorem [1]. Well, at least for ordinal (ranked) voting systems. Watch the video below to get a popular summary on "why?".
By the end of the video a possible solution is discussed. Instead of using ranked voting systems we should use rated voting systems, as first shown by D. Black [2]. I feel a bit skeptical about this, as lots of people would likely get confused over what should they write in their ballots. Furthermore, I am not sure if such voting is impervious to strategic voting and would encourage truthful statement of the preferences. Still, maybe?
References
- K. J. Arrow. A difficulty in the concept of social welfare. Journal of Political Economy 58: 328-346 (1950). doi: 10.1086/256963.
- D. Black. On the Rationale of Group Decision-making. Journal of Political Economy 56(1): 23-34 (1948). doi: 10.1086/256633.
