George Masterton

Linking as voting: how the Condorcet jury theorem in political science is relevant to webometrics

A webmaster’s decision to link to a webpage can be interpreted as a “vote” for that webpage. But how far does the parallel between linking and voting extend? In this paper, we prove several “linking theorems” showing that link-based ranking tracks importance on the web in the limit as the number of webpages grows, given independence and minimal linking competence. The theorems are similar in spirit to the voting, or jury, theorem famously attributed to the 18th century mathematician Nicolas de Condorcet. We argue that the linking theorems provide a fundamental epistemological justification for link-based ranking on the web, analogous to the justification that Condorcet’s theorems bestow on majority voting as a basic democratic procedure. The analogy extends to the practical limitations facing both kinds of result, in particular due to limited voting/linking independence. However, we argue, referring to the theoretical developments inspired by the jury theorem, that some of the pessimism expressed in the webometrics literature regarding the possibility of a “theory of linking” may be unjustified. The present study connects the two academic disciplines of webometrics in information science and epistemic democracy in political science by showing how they share a common structure. As such, it opens up new possibilities for theoretical cross-fertilization and interdisciplinary transference of concepts and results. In particular, we show how the relatively young field of webometrics can benefit from the extensive and sophisticated literature on the Condorcet jury theorem.

Topological variability of collectives and its import for social epistemology

Social epistemology studies knowledge and justified belief acquisition through organized group cooperation. To do this, the way such group cooperation is structured has to be modeled. The obvious way of modeling a group structure is with a directed graph; unfortunately, most types of social cooperation directed at epistemological aims are variably implementable, including in their structural expression. Furthermore, the frequency with which a practice is implemented in a certain way can vary with topology. This entails that the topology of social practices directed toward epistemological ends has to be modeled by a set of directed graphs, or their equivalent, together with a probability distribution over that set. In theory, this is eminently possible; however, there are considerable practical obstacles to the specification of a practice’s topology in this way. This paper examines these practical difficulties and concludes that todays sampling protocols are either far too slow to handle pratices with 10 or more participants, or else prone to produce misleading evaluations.

What to do with a forecast

In the literature one finds two non-equivalent responses to forecasts; deference and updating. Herein it is demonstrated that, under certain conditions, both responses are entirely determined by one’s beliefs as regards the calibration of the forecaster. Further it is argued that the choice as to whether to defer to, or update on, a forecast is determined by the aim of the recipient of that forecast. If the aim of the recipient is to match their credence with the prevailing objective chances, they should defer to the forecast; if it is to maximize the veritistic value of their beliefs, they should update on the forecast.

The Only Probability is Verbal Probability

Abstract In 1977 van Fraassen showed convincingly, and in detail, how one can give a dissentive answer to the question “[a]re there necessities in nature?”. In this paper, I follow his lead and show in a similar fashion and detail, how it is possible to give a dissentive answer to: Are there probabilities in nature? This is achieved by giving a partial analysis – with the aid of Kaplanian pragmatics – of objective chance in terms of that credence that is reasonable where prevailing laws and conditions exhaust one’s evidence. This template belongs firmly within the established Bayesian program of analysing objective chance as ultimate belief. Its contribution to that program is the same as van Fraassen’s contribution to the empiricist program of analysing physical necessity; namely, it demonstrates the logical possibility of such an analysis.