more on reasonable voting schemes

The above paper is on topics very similar to what we covered in class. In this paper, the authors analyze Arrow's Theorem on Single peaked domains. Thus, this paper describes the topics that we learned in class in more detail. It focuses specifically on Single Peaked preferences in light of Arrow's theorem. Arrow's Theorem states that given that there are at least three alternatives and at least two individuals that choose between all the alternatives, than a dictatorial preference is the only Pareto efficient preference aggregation rule.
The second theorem (Black's Theorem) covered in this paper states that if individual preferences are single peaked, then majority rule is a non-dictatorial preference aggregation rule that satisfied independence of irrelevant alternatives.
These two theorems go hand in hand with the 'reasonable voting schemes' that we discussed in lecture. In this paper, different notations are used in order to explain these principles in a clearer fashion. I found this both helpful and interesting. In addition, through the analysis with the use of the stated theorems, useful and interesting conclusions are made. One of the conclusions the authors make is that
"while the ordering of preferences over the marginal rate of a flat income tax may be presumed (with at least some implicit heroism) to be single-peaked according to the usual ordering of
the real line, the general presumption that preferences are single-peaked with respect
to a set of political alternatives does not provide enough information to declare what
the “median most-preferred alternative” is, even after individuals have informed you of
their most-preferred alternatives."
I would recommend this paper to anyone interested in reading more about reasonable voting schemes that we started discussing in class.

Below is the link:
http://www.princeton.edu/~pegrad/papers/patty2.pdf