Imagine we want to build a new space port at one of four recently settled Martian bases, and are holding a vote to determine its location. Of the hundred colonists on Mars, 42 live on West Base, 26 on North Base, 15 on South Base, and 17 on East Base. For our purposes, let’s assume that everyone prefers the space port to be as close to their base as possible, and will vote accordingly. What is the fairest way to conduct that vote?
Zamislite da hoćemo da izgradimo novo svemirsko pristanište u jednoj od četiri nedavno naseljene baze na Marsu, i sprovodimo glasanje da bismo mu odredili lokaciju. Od stotinu kolonista Marsa, njih 42 živi u Zapadnoj bazi, 26 u Severnoj bazi, 15 u Južnoj bazi i 17 u Istočnoj bazi. Za potrebe ove situacije, pretpostavimo da svima odgovara da pristanište bude što je moguće bliže njihovoj bazi i da će glasati shodno tome. Koji je najpravedniji način za sprovođenje tog glasanja?
The most straightforward solution would be to just let each individual cast a single ballot, and choose the location with the most votes. This is known as plurality voting, or "first past the post." In this case, West Base wins easily, since it has more residents than any other. And yet, most colonists would consider this the worst result, given how far it is from everyone else. So is plurality vote really the fairest method?
Najjednostavnije rešenje bi bilo dozvoliti svakom pojedincu da da jedan glas, i odabrati lokaciju koja ima najviše glasova. To je poznato kao većinsko ili pluralno glasanje. U ovom slučaju, Zapadna baza lako pobeđuje, jer ima više stanovnika od ostalih. A ipak, većina naseljenika bi to smatrala najgorim rezultatom, s obzirom na njenu udaljenost od svih ostalih. Dakle, da li je većinsko glasanje zaista najpravedniji metod?
What if we tried a system like instant runoff voting, which accounts for the full range of people’s preferences rather than just their top choices? Here’s how it would work. First, voters rank each of the options from 1 to 4, and we compare their top picks. South receives the fewest votes for first place, so it’s eliminated. Its 15 votes get allocated to those voters’ second choice— East Base— giving it a total of 32. We then compare top preferences and cut the last place option again. This time North Base is eliminated. Its residents’ second choice would’ve been South Base, but since that’s already gone, the votes go to their third choice. That gives East 58 votes over West’s 42, making it the winner. But this doesn’t seem fair either. Not only did East start out in second-to-last place, but a majority ranked it among their two least preferred options.
Šta ako bismo probali sistem poput rangiranog glasanja koje uzima u obzir pun spektar preferencija ljudi, umesto samo njihove glavne izbore? Evo kako bi to izgledalo. Najpre, glasači rangiraju sve opcije od prve do četvrte, i uporedimo njihove glavne odabire. Jug dobija najmanje glasova za prvo mesto, pa biva eliminisan. Njegovih 15 glasova se dodeljuje drugom izboru tih glasača - Istočnoj bazi - koja time dobija 32 glasa. Zatim uporedimo glavne preferencije i ponovo odbacimo opciju na poslednjem mestu. Ovoga puta je Severna baza eliminisana. Drugi izbor njenih glasača bila bi Južna baza, ali pošto je ona uklonjena, glasovi idu trećoj opciji. Time Istok dobija 58 glasova, naspram 42 glasa Zapada, i postaje pobednik. Ali ni to ne deluje fer. Ne samo da je Istok počeo na pretposlednjem mestu,
Instead of using rankings, we could try voting in multiple rounds, with the top two winners proceeding to a separate runoff. Normally, this would mean West and North winning the first round, and North winning the second. But the residents of East Base realize that while they don’t have the votes to win, they can still skew the results in their favor. In the first round, they vote for South Base instead of their own, successfully keeping North from advancing. Thanks to this "tactical voting" by East Base residents, South wins the second round easily, despite being the least populated. Can a system be called fair and good if it incentivizes lying about your preferences?
već ga je većina rangirala među dve najmanje poželjne opcije. Umesto rangiranja, mogli bismo pokušati sa glasanjem u više krugova, pri čemu će dva glavna pobednika preći u zaseban krug. To bi trebalo da znači da će Zapad i Sever pobediti u prvom krugu, i da će Sever pobediti u drugom. Ali stanovnici Istočne baze shvataju da, iako nemaju dovoljno glasova da bi pobedili, i dalje mogu da okrenu rezultate u svoju korist. U prvom krugu glasaju za Južnu bazu umesto za svoju, čime uspešno sprečavaju da Sever prednjači. Zahvaljujući ovom „taktičnom glasanju” stanovnika Istočne baze, Jug lako pobeđuje u drugom krugu, uprkos njegovoj najmanjoj naseljenosti. Da li se sistem može nazvati pravednim i dobrim ako podstiče laganje
Maybe what we need to do is let voters express a preference in every possible head-to-head matchup. This is known as the Condorcet method. Consider one matchup: West versus North. All 100 colonists vote on their preference between the two. So that's West's 42 versus the 58 from North, South, and East, who would all prefer North. Now do the same for the other five matchups. The victor will be whichever base wins the most times. Here, North wins three and South wins two. These are indeed the two most central locations, and North has the advantage of not being anyone’s least preferred choice.
u vezi sa preferencijama? Možda bi trebalo da dozvolimo glasačima da se izjasne šta bi više želeli u svakom mogućem suprotstavljenom paru. To je poznato kao Kondorseov metod. Uzmimo jedan par: Zapad naspram Severa. Svih 100 kolonista glasa između njih dvoje. U tom slučaju bi za Zapad glasalo 42, dok bi 58 glasova dali Sever, Jug i Istok, a koji su za Sever. Sada uradimo isto za ostalih pet parova. Pobednik će biti onaj čija baza pobedi najveći broj puta. Tako Sever pobeđuje tri puta, a Jug pobeđuje dva puta. To zaista jesu dve najznačajnije lokacije,
So does that make the Condorcet method an ideal voting system in general? Not necessarily. Consider an election with three candidates. If voters prefer A over B, and B over C, but prefer C over A, this method fails to select a winner.
i Sever ima tu prednost da nije ničiji najmanje omiljeni izbor. Da li to znači da je Kondorseov metod, opšte uzev, idealan sistem glasanja? Ne nužno. Uzmimo glasanje između tri kandidata. Ako su glasači više za A nego za B, i više za B nego za C, ali više za C nego za A,
Over the decades, researchers and statisticians have come up with dozens of intricate ways of conducting and counting votes, and some have even been put into practice. But whichever one you choose, it's possible to imagine it delivering an unfair result.
ovaj metod neuspešno bira pobednika. Kroz decenije, istraživači i statističari su smišljali desetine složenih načina sprovođenja glasanja i brojanja glasova, od kojih su neki bili i primenjeni u praksi. Ali koji god da odaberete,
It turns out that our intuitive concept of fairness actually contains a number of assumptions that may contradict each other. It doesn’t seem fair for some voters to have more influence than others. But nor does it seem fair to simply ignore minority preferences, or encourage people to game the system. In fact, mathematical proofs have shown that for any election with more than two options, it’s impossible to design a voting system that doesn’t violate at least some theoretically desirable criteria. So while we often think of democracy as a simple matter of counting votes, it’s also worth considering who benefits from the different ways of counting them.
moguća je pretpostavka da će dati nepravedan rezultat. Ispostavlja se da naš intuitivni koncept pravičnosti u stvari obuhvata više pretpostavki koje mogu biti oprečne. Ne čini se pravednim da neki glasači imaju veći uticaj od drugih. Ali ne deluje fer ni da se preferencije manjina prosto ignorišu, niti da se ljudi podstiču da nameštaju sistem. Zapravo, matematički dokazi su pokazali da je u slučaju svakog izbora koji ima više od dve opcije nemoguće osmisliti sistem glasanja koji ne narušava bar neke teoretski poželjne kriterijume. Iako često smatramo da je demokratija prosto stvar prebrojavanja glasova,