Introduction

In this chapter we review all remaining published and developed cycle claims that I could find in the literature, as well as some undeveloped cycle claims. Blydenburgh (1971), influenced by Arrow and Riker, sought to demonstrate a cycle in deliberations on the Revenue Act of 1932 in the US House of Representatives. The vote was among a sales tax, an income tax, and an excise tax. Blydenburgh's first argument is that a majority was against each alternative. A majority voted for the excise tax, however; and Blydenburgh's inference that a majority nevertheless had preferences against the excise tax is in error arising from confusion about which alternative is pitted against which. The second argument makes two assumptions in order to obtain complete inferred preferences from incomplete revealed preferences. The first assumption is arbitrary and weakly warranted, however, and further, Blydenburgh, without explanation, inconsistently applies the second assumption; if the first assumption is dropped, or if the second assumption is consistently applied, then he has no cycle. His third argument again errs due to confusion about which alternative is pitted against which; and ultimately reduces to the failed second argument. Blydenburgh's erroneous analysis is frequently cited by partisans of the irrationalist doctrine.

Bjurulf and Niemi (1978) explore Rikerian doctrine in the records of the Scandinavian parliaments. They claim to find three cycles. The first concerns the construction of a hospital. In order to show a cycle they must go beyond expressed votes and infer some of the individual preference rankings.