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ECONOMICS 310 XD Home Assignment CHAPTER 22 FRONTIERS OF MICROECONOMICS , 477 (P.2/3) Spring 2020 4029. ....... . . in the news T NEWS compete again if none receives a majority that he speculates would have won head to Sports fans ay manipulation when votes Journ of the vole. Among the potential problems, head. don't go as they'd hoped. Mary sports showing up to vote loi your favorite cand date How this works out In reality is hard to awards and rankings are der'ved from what may create a worse outcome than not know, because the Academy doesn't release is known as a Barda count, which asks voters Arrow's Problem in Practice showing up at all For example, your vate any details about the balloting, even after to rank candidates and then asigns points could change the order'n which candidates the telecast, In part to wold shaming fifth- on a sliding scale, with the most for first Voting systemus matter not only for choosing political leaders but also we ellminated, and the next-in-line candi- place films. Mr. Davis says even he never place votes and the least for last place ones. for awarding prizes. face on the ba lot for the newly eliminated learns the numbers from his accountants: Critics of these systems fear that stra i'm may be a film you loathe. "Are there years when I'm curlous as to Irgic voters wil abign their top choke To choose Oscar winners, voters simply what the order of finish was? Absolutely. the highest possible score, and everyone And the Oscar Goes College in 2000 if Ralph Nader hadn't that cilferent: The candidate with the high choose their favorite from the nowknees, But I recognize it as a valger curiosity In else zero, thereby seaing more power than diverted more votes from him than he took cut average, or mean, score wins. and the contender with the most votes wins. mysell" to .. Not Its Voting That could fever a film that has a devoted Such secrecy frustrates voting theorats voters who approach the system earnestlye ram former President George W. Bush. or, In the case of rankings, bury or amit a "It's crazy, " says Michel Balinski, profes- Yet the second 'system's leading advo- action of fans, and sink films with overlap- who are anxious for experimental data preferred candidate's top rival. Boston Red System cate. Temple University mathematician ping folowings who spit their vote. Even abo. voter behavior that may help them Soo fans will tell you to this day that such BY CARL BIALIK sor of research at Ecole Polytechnique In Warren D. Smith, has devoted a Web pa: strategic voting by a New York beat writer Paleseau, France. The nomination system's to the Balinks!-Larakj system's "numerous cost crites of instant runall say It beats choose from among different voting sys Academy Award nominees and winners disadvantages." this plurality system that led to the Gore- tems. Without such evidence, they are felt cost Pedro Martinez the American League properties are "truly perverse and entithell- Most Valuable Player award a decade ago. are selected using two dillerent voting cal to the idea of democracy, " says Steven Braps, professor of politics at New York Brace yourselves for "Ishtar" deleating Nader-Bush lesill In the film realm, Prof. to devise ther own studies, to dream up exams of NYU blames the current system guar ples that sick rival systems or to create Says Prof. Baines, "Not everyone will "The Godfather." Suppose 49 voters award do it, but enough will do it to maripolate systems that are, according to some political mathematicians, the worst way to convert University. He thinks the fnal vote for the "The Godfather" six points and "Ishtar" or the best-picture victory of "Rocky" over computer simulations to study how easily Oscar winner may be even worse than the only four. One voter grants the desert films such as "Network" and "Taxi Driver" different systems can be manipulated. the msuits." roles' preferences Into an election outcome. selection of nominees. The nominees are selected using a system debacle four points and the malia master called instant runol, which has been adopted The big problem: If voting systems them- piece three, and the remaining 49 awar selves were put to a vote, prominent schol- "The Godfather" three points and "Ishear" Choosing a Winner : Conducting and deciding a vote using an instant runoff h some municipal and state elections. Out ais would each produce a different ballot, of last year's 281 eligible films, each voter only one point. "Ishtar" actually wins wit STAGE 3 selects five nominees In order of preference then disagree about which system should be STAGE 1 STAGE 2 for, say, best picture. All movies without any used to select the winner. So it's no surprise a median score of four points compared to "The Godlather's" three polnts. Prof. D has the Now & bar that advocates of alternate voting systems, Balingld, In tom, calls range voting a "ild :. Vows a' which range from simple yesino approval lous method," because it can be manipu asked to fewest voll first-place votes are eliminated. The votes for Just place those films with the least flost pace votes ate e-assigned until five nominees have enough. ratings to assigning numerical scores to andidales each candidate, have had title more luck laned by strategic voters. Despite the flaws In Oscars voilng, the So D because C wales get want the thad w ww ww One problem with that system is a kind reforming political elections than they have system remains as it has since 1936. Every After the of squeaky wheel phenomenon: A movie with entertainment awards, 15 years or so, the Academy,go-examines its ranking. reassigned to shake of the that is second place on every ballot wil lose Consider two systems that, on the sur- voting and has decided to stick with it, says no candidate the second voters an out to one that ranks first en only 20%% of face, seem similar, Prof. Ballnid and muth- the uccend the Academy of Motion Picture Arts and has a choice on those ballots, C. choice, D. has ballots but is hated by everyone else. Then, emailian Ride Larski have devised a system Sciences" executive director, Bruce Davis. " 11 2 Now Chas five bean in another upside-down outcome, a movie they call majority judgment that requires is a very effective method of reflecting the he lead UUNNNNNNNNNB www wwwwwwn No. 1 rankings can win for best picture even if 79% of voters to rank each candidate on a scale will of the entire electorate, " Mr. Davis say's voters hated it so long as they split their from 1 to 6. The votes are lined up in order, 12 30 A and Care C beats A votes evenly among the losing films. This and each candidate is assigned the middle, But many voting theorists aren't so kee" 13 lied, nine votes on the system. It's caled Instant runcli 14 aww WW isn't as unfamiliar as it sounds: Some people or median, score. The highest median score think Al Gore would have won the Electoral w because it is used in political elections in I ev wins. Another system, range voting, isn't of a two-stage vole in which top candidates The original votes for 14 candidates are shown in Source: The Wall Sover Junk Asbury $ 1:01. the Stage I columns, Note lowest numbers shown indicate the must preferredcandidates. ( @ ) Explain why to arrive at stage 2, D'svotes are allocated to C, while to arrive at stage 3, BS votes are allocated to C, in the "instant runoff "method in the article. ( b) Pairwise majorityvoting. consider all possible matchups at pairs of candidates and identify winners. Determine the hierarchy of preferences . Arethere any inconsistencies or transitivities in preference rankings? Is there a clear winner? Are there any ambiguities among candidate rankings? (c ) Borda count. Assign Borla points and determine the winning candidate by this method. Note that unlike the listing above, higher Borda point numbers are assigned to most preferred candidates. What's the total Borda count of all candidates together
