What can be learned from failed proofs of non-theorems?

This paper reports an investigation into the link between failed proofs and non-theorems. It seeks to answer the question of whether anything more can be learned from a failed proof attempt than can be discovered from a counter-example. We suggest that the branch of the proof in which failure occurs can be mapped back to the segments of code that are the culprit, helping to locate the error. This process of tracing provides finer grained isolation of the offending code fragments than is possible from the inspection of counter-examples. We also discuss ideas for how such a process could be automated.

Don’t expect me to vote for you just because I like you, even if you do make me feel warm inside: a comparison of the validity of non-ipsative measures of party support

The inclusion of non-ipsative measures of party preference (in essence ratings for each of the parties of a political system) has become established practice in mass surveys conducted for election studies. They exist in different forms, known as thermometer ratings or feeling scores, likes and dislikes scores, or support propensities. Usually only one of these is included in a single survey, which makes it difficult to assess the relative merits of each. The questionnaire of the Irish National Election Study 2002 (INES2002) contained three different batteries of non-ipsative party preferences. This paper investigates some of the properties of these different indicators. We focus in particular on two phenomena. First, the relationship between non-ipsative preferences and the choices actually made on the ballot. In Ireland this relationship is more revealing than in most other countries owing to the electoral system (STV) which allows voters to cast multiple ordered votes for candidates from different parties. Second, we investigate the latent structure of each of the batteries of party preferences and the relationships between them. We conclude that the three instruments are not interchangeable, that they measure different orientations, and that one –the propensity to vote for a party– is by far preferable if the purpose of the study is the explanation of voters’ actual choice behaviour. This finding has important ramifications for the design of election study questionnaires.