问题如下：
The topic of another lecture is prospect theory. Liu presents the students with the following two situations and asks them if they would accept or reject each one:
Situation 1 A 50% probability of winning $10,000 and a 50% probability of losing $4,000
Situation 2 A 50% probability of winning $10,000 and a 50% probability of losing $8,000
The students vote to accept Situation 1 but reject Situation 2. Liu then presents a third situation:
Situation 3 Choosing between losing $12,000 with 100% certainty, or accepting a gamble that offers a 50% probability of winning $6,000 and a 50% probability of losing $24,000
The students vote to accept the gamble in Situation 3.
Explain how the voting results in each of the three situations are consistent with prospect theory.
i.Accepting Situation 1
ii.Rejecting Situation 2
iii.Accepting the gamble in Situation 3
选项：
解释：
Prospect theory is an alternative to expected utility theory. This theory describes how individuals make choices in situations in which they must decide between alternatives that involve risk and how they evaluate potential losses and gains. Prospect theory considers how alternatives are perceived based on their framing, how gains and losses are evaluated, and how uncertain outcomes are weighted.
i. Accepting Situation 1
Most people reject a gamble with even chances to win and lose unlessthe possible win is at least twice the size of the possible loss.
In this gamble, the possible win is 2.5 times the possible loss, so the student vote to accept Situation 1 is consistent with prospect theory. Accepting Situation 1 is consistent with prospect theory because experimental evidence shows that most people reject a gamble with even chances to win and lose, unless the possible win is at least twice the size of the possible loss.
ii.Rejecting Situation 2
Most people reject a gamble with even chances to win and lose unlessthe possible win is at least twice the size of the possible loss.
In Situation 2, the chances to win and lose are the same but the possible win is only 1.25 times the possible loss. Thus the student vote to reject Situation 2 is consistent with prospect theory.
Rejecting Situation 2 is consistent with prospect theory because experimental evidence shows that most people reject a gamble with even chances to win and lose, unless the possible win is at least twice the size of the possible loss. In Situation 2, the possible win is only 1.25 times the possible loss, so the student vote to reject the investment is consistent with prospect theory.
iii.Accepting the gamble in Situation 3
People are risk-seeking when there is a low probability of gains or a highprobability of losses.
Deviations in decision making result in overweighting low-probability outcomes.
The gamble may appear more attractive than the sure loss, so the student vote to accept the gamble is consistent with prospect theory. Experimental evidence shows that risk-seeking preferences are held by a large majority of people when there is a low probability of gains or a high probability of losses. Therefore, the student vote to accept the gamble over the sure loss in Situation 3 is consistent with prospect theory.
为神马结果选择situation1,而不是situation2，
答案不能用cancellation 解释？因为在win的概率相同的情况下，可以只考虑输的概率cancellation ，此时找输的最少的即可。
