Sunday, October 5, 2008
Questions...........
can someone please briefly explain the concept of the Condorcet Paradox or Cycle? What does it really explain/describe? What if one voting does not have a condorcet paradox or a so called condorcet loser? How does it matter and what does it affect? How is it really implied besides in theory? In addition, can someone briefly explain/describe the voting process of the STV system? How is the dhont method and the hare method used? I didnt really understand how those work? In addition, how exactly that majority will does not exist? how can their be no majority will? there certainly exist majority will in our world. Thanks.....
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6 comments:
I'm sure that you have this definition from the powerpoint, but Professor King explains the Condorcet Paradox to be: The collective preference set of a group of rational individuals can itself be irrational. In other words, a single, obvious, and unambiguous “majority will” does not exist.
Based on some further reading, i think that the condorcet paradox explains that:
a) majority will is impossible to determine because people have varying preferences, and sometimes it is impossible to see how the preference of a society is arranged. Preference in this case is meant to find the winner who is preferred by the most voters and is the least disliked by voters. As such, it isn't always clear who the winning candidate should be.
b) people's wishes and majority will can be conflicting.
My take on your majority will question is this (I'm not sure if it is right, but this is how i interpret what we've read): Majority will does not necessarily exist in our world because it is not always true that a simple majority of people want the same thing. People's preferences are not necessarily rational, and therefore do not always benefit society. This is where there is a similar debate as with the idea of what representation means - efficiency of government, or true representation of the people. In the same way, should majority will represent the desires of individuals in society OR their best interests? These two do not necessarily overlap, so majority will is somewhat ambiguous.
How STV works-
1) Calculate minimum number of votes necessary to gain a seat. In our example, we used the Droop Quota - [V/(S+1)]+1, where V is the total number of valid votes, and S is number of seats available
2) Calculate number of votes for each candidate based on first choice only
3) If a candidate's votes reaches [V/(S+1)]+1, award that party a seat.
4) If a candidate has reached the quota, next you will recalculate votes – taking ‘extra ballots’ from the first party (the number of votes it has over the quota), and sort them by second choice among the next group of candidates.
If a candidate does not reach the quota based on first choice preferences, take the candidate with the least number of votes, and redistribute those votes based on second choice preference.
5) If this does not result in another seat being won, continue to take the party with the least number of votes and redistribute those based on second choices until the next seat is won.
6) Continue this process until all seats are taken
oh wow, thanks alot. this is helpful. i needed someone to reassure me with the answers. thanks
To add to the explanation of Condorcet's Paradox, I think that it is also has a strong connection to Arrow's Theorem. Societies are faced with a trade-off when they implement a certain voting system; they must either restrict the expression of preferences or deal with an irrational outcome. Condorcet showed how the overall preferences of a simple society could be irrational when they are not restricted, and therefore we can see that this system is not exactly fair for society as a whole.
Now that I've done more studying, here's my take on the condorcet paradox:
In a group of rational people, a rational collective preference is not necessarily reached.
As such, there is not single, obvoius and unambiguous majority will.
This is where Arrow's Theorem comes in -
In order to avoid an irrational outcome/choice, the preferences of the individuals must be restricted.
also on STV: i was confused about this for a while, in an STV electoral system, the most seats any one party can get in a district is one; once it has won a seat, all of its votes are re-distributed. I believe at the end the seats won by parties are proportionately distributed in parliament.
To add to the Condorcet discussion, in addition to the yielding an irrational preference set, different voting methods (plurality v. pairwise voting) can yield rational but different preference sets in more complex societies. If both preference sets are rational, how is one to claim that they both represent the majority will?It is this paradox that enables Arrow to claim that institutions (ie, voting methods) are necessarily formative of whatever "majority will" a certain society produces.
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