The international olympic committee consists of 55 members and is selecting the host city of the next summer games. There are five candidate cities: Budapest (B), Doha (D), Paris (P), Rome (R), and Seoul (S). The individual preferences are: 18 members have ranking RP SBD, 12 members have ranking DSP BR, 10 members have ranking BDSP R, 9 members have ranking P BSDR, 4 members have ranking SDP BR, and 2 members have ranking SBP DR. (1) Is there a Condorcet winner? Justify your answer. (2) What is the social preference according to Borda count rule? (3) Under Borda count rule, does any member have an incentive to behave strategically? That is, given all other 54 members report their true preference rankings, does any one have an incentive to misrepresent his/her true preference ranking and achieve a better outcome? Justify your answer. (4) Now consider the following rule: each member casts two votes, one for his/her favorite Asian city (D or S), and the other for his/her favorite European city (B, P or R). For example, a member whose preference is RP SBD will cast one vote for Rome and one vote for Seoul. Count the total number of votes