Over two centuries of theory and practical experience have taught us that election and decision procedures do not behave as expected. Instead, we now know that when different tallying methods are applied to the same ballots, radically different outcomes can emerge, that most procedures can...

A surprise is how the complexities of voting theory can be explained and resolved with the comfortable geometry of our three-dimensional world. This book is directed toward students and others wishing to learn about voting, experts will discover previously unpublished results. As an example, a...

Electing a committee introduces constraints beyond excellence, such as ensuring a balance of gender, tenure, talent, and other characteristics. The difficulties are captured by an actual example where every voter desired gender diversity on a committee and voted accordingly, but only men were...

Brams, Fishburn, and Merrill (1988) contend that the indeterminacy of approval voting (AV), introduced in our paper (1988), is not a vice, but a surpassing virtue of AV. They do not compare the negative versus the positive features of AV, so their assertion remains a conjecture. Our response...