search engine—as I just did. Back came a list of sixty-one papers, the
most recent being this year, and the earliest in 1975. If the paper was
synopsized in Math Reviews, it can be obtained and read almost immedi-
ately.
This process has made mathematical research much more efficient—
and frenetic. The number of publications has jumped exponentially. In
addition, the Internet has enabled communication between mathemati-
cians in all parts of the world who might never have come into contact. I
have recently collaborated with mathematicians in Germany, Poland,
and Greece whom I never would have met (barring a chance meeting at
a conference) were it not for the Internet.
MathSciNet also reveals an interesting divergence between the present
state of affairs vis-à-vis the Gibbard-Satterthwaite theorem and the Balin-
ski-Young theorem. Insincere voting is related to bluffing in poker; and
strategy is a key aspect of game theory, an area of mathematical econom-
ics which has resulted in several Nobel Prizes. Of particular interest at
the moment is research into areas in which information may or may not
be public, such as computing the transactional costs in routing networks.
In such a network, the owner of a link is paid for the link’s use. A user of
the network wants to obtain information, which must be transmitted
through a succession of links, at the minimum cost; one obvious strategy
is simply to ask the cost of each link. However, the owner of a link may
profit by lying about the cost of using his link; this is similar to insincere
voting. A key idea being explored is games that are strategy proof; that is,
those in which there is no incentive for a player to lie about or hide infor-
mation from other players. It is easy to see how this is related to voting.
On the other hand, only twenty-two articles are listed on MathSciNet con-
cerning the Balinski-Young theorem, the most recent being in 1990. The
field is evidently dormant, despite the fact that there is an obvious gap in
the area; I have not been able to find any work incorporating the new states
paradox in Balinski-Young type theorems. Nonetheless, because of the im-
portance of the Electoral College, the current (Huntington-Hill) method of
selecting representatives is currently being investigated^8 by mathemati-
cians and political scientists to see if better methods are available.
As is often the case, when an ideal result is shown to be impossible, it is
important to develop criteria for the evaluation of what can be achieved
under various circumstances. An impossible result establishes budgetary
constraints, and it is up to us to determine what to optimize, and how to
accomplish that, while living within our budget.
The Smoke- Filled Rooms 235