H. Reiju Mihara, who has an Erdos number of 3 (via Erdos to A. L. Rubin to N. Brunner), is one of the four voting theorists (along with Condorcet, Borda, and Arrow) referred to in an article in The Why Files, a science education site founded as a project of the National Institute for Science Education.
Mihara's works have been cited in books on various subjects, including social choice theory, mathematics, history of economics (cybernetics), and philosophy of science. Here is an example. Apparently, he needs more!
: Provided that you reasonably respect my rights, you are encouraged to make references and links to these pages (http://www5.atwiki.jp/reiju/ and below). Some characters on this page will not appear correctly if your system cannot handle Japanese properly. In that case, just ignore them. (Even if they appear correctly, they are not likely to make sense to you unless you can read Japanese.) [リンクは大歓迎．]
FAQs (research) answers some questions about
You can find a precise statement of the theorem and a brief proof, too.
When I'm asked what my specialization is, I usually answer normative economics ---an area of economics (?) concerned with value judgments ("what is good?" or "what should be done?"). Since economics has "officially" been a value-free science (that is, it avoids value judgments), normative economics has conventionally adopted a certain trick. Instead of saying that a certain policy is good, it used to say "if your goal is such and such (this part contains value-judgments), then this policy works." Well...fine. But can economics really be value-free? Is it really important to be so?
The fact is that in the conventional normative economics (usually called "welfare economics"), the "if" part (a performance criterion) has almost always been concerned with efficiency. (Economists say a certain situations "efficient" or "Pareto-optimal" if there is no alternative situation that is preferred by everybody.) Maybe we'd better consider other criteria, too. Fortunately, social choice theory (or its descendant), traditionally a minor area in economics(?), offers many different criteria. These criteria include (i) whether the society treats individuals equally, (ii) whether information available in the society is efficiently used, (iii) whether the society adopts rules likely to be followed by many people (doesn't the society ignore individuals' incentives to exploit the rules?), (iv) whether the society respects individual's freedom of choice? Choosing from these and other performance criteria, or deciding what criteria to emphasize, is an activity that cannot always be value-free. As I understand, normative economics (i) recognizes the impossibility of a value-free social science, but (ii) does not particularly view this impossibility negatively, and (iii) even positively gets involved with value judgments.
Normative economics belongs to the intersection of several disciplines---including ethics and economics. Most of my work, however, is (and will probably be) rather mathematical, reflecting my training in Minnesota as an economic theorist. In particular, I adopt an axiomatic approach extensively used in social choice.
My current research is concerned about information processing in social choice. Though it may not sound particularly normative, its intellectual background dates back to the debate on the possibility of socialism. In the debate, F.A. Hayek insisted that socialism would not work since it could not efficiently make use of dispersed information available to individuals. Although I do not think that is the most important reason for the failure of socialism, I think it is an important one. I applied theory of computation to examine possibility of centralized decision making.
"Arrow's Impossibility Theorem and ways out of the impossibility" gives a ten-minute introduction to social choice theory. It also touches on some recent developments:
"King Solomon's Dilemma: A simple solution" analyzes the Judgment of Solomon in the Old Testament. (My YouTube debut):
Young 1994 Materials. A set of lecture notes for courses based on H. Peyton Young, Equity: In Theory and Practice (Princeton University Press, Princeton, 1994). In the past, I got requests from the former political prisoner Marek Kaminski as well as the author H. P. Young. (You may also want to check, for example, Tayfun Sonmez's Game Theory, Lectures 11-14.)