[EM] Cramster question

[Michael Rouse]

I was idly doing a Google search for "Condorcet Plurality," and up 
popped a question on a site called Cramster (I have no clue what the 
site is about, it just came up in the search). Someone a couple of weeks 
ago asked:

*Question Details:*

Condorcet’s method has many nice properties, and some supporter’s of 
former Vice President Al Gore pointed out that Al Gore was very likely 
the Condorcet winner. The problem with Condorcet’s method is that it 
does not produce

a winner often. Thus, let us propose a combination of the Condorcet’s 
method and the plurality system: This combined system deems the 
Condorcet winner as the winner. In case that the Condorcet’s method does 
not produce a winner, then use plurality method to select the winner.


1) Does the Condorcet-plurality system produce winner more often than 
Condorcet’s

method? Explain.

2) Does the Condorcet-plurality system satisfy the Pareto condition? 
Explain.

3) Does the Condorcet-plurality system satisfy Condorcet winning 
Criterion? Explain.

4) We know that both Condorcet and plurality systems are monotone. Is 
the Condorcet-

plurality combined system still monotone? Explain.

5) Is the Condorcet-plurality system manipulable? If your answer is 
manipulable,

give an example of an election where manipulation can be done. If your 
answer is not

manipulable, prove it.


Here is the link: http://qaboard.cramster.com/other-topic-5-551512-cpi0.aspx

Hmm, looking at it again, it may be a homework site. Anyway, such 
questions often bring up interesting discussions on the EM list, so I 
thought I'd let people know.

Michael Rouse

PS If the text is scrambled, let me know. I cut and pasted an html document.