1 best real life example for a failure of completeness 2 bes

1) best real life example for a failure of completeness

2) best real life example for a failure of transitivity

3) best real life example for a failure of monotonicity

Solution

1. Consider a taxi driver Ben who wants to be scientist or a Neurosurgeon. Both the options are practically infeasible. Now, is false that Ben prefers becoming a Scientist to becoming a neurosurgeon and it is also false that he prefers becoming a neurosurgeon to becoming a scientist. But it is also not true that he is indifferent between becoming a neurosurgeon and a scientist.

2. 2. Consider an individuals tied to a machine, which gives electric shocks.where each sucessive shock is greater than the previous one. . Now suppose , the individual is offered $200 to move up to the next, than means tolerating a shock gives him a return of n$200. It is rational for him prefer shock n+1 to shock n as he gets increased monetory benifits. but he will not prefer setting 1,000 to setting 0 it may take his life and no amount of money can make up for it.

3. Monotonicity fails in voting system sometimes. Consider A, B and C are participating in an election. In round 1, candidate A wins C wins the election with 201 votes , candidate B receives 100 votes and candidate gets 99 votes. Clearly A gets eliminated.

Now suppose two other people participate who did not participate earlier. Thier preference ordering is A > B > C. Now,andidate C still wins the first round with 201 votes, but candidate B is eliminated since A now receives 101 votes while B gets 100 as before. In this case, the participants actually caused their preffered candidate to loose in the election by participating.