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Voting and MCDM: the pedagogy of the Saari triangle

Hakula Jaakko

Control and Cybernetics

2021

Vol. 50, No. 3

401--412

The essay has a twofold objective: primarily, to present an application of voting theory as a possible evaluation method, and concurrently, to offer a pedagogic framework, based on that very application. Evaluation and certain notions of preference and value have common semantic roots. By equating preference and choice, we end up amidst social choice (SC) theory and voting methods, also manageable as joint decisions in multiple-criteria decision making (MCDM). With the aid of the Saari triangle some essential differences of pairwise and positional voting rules for up to three alternatives can be depicted. A voting or decision rule does not necessarily follow the true preferences of the actors, but may mirror the problematics of the chosen rule. The Saari triangle makes it possible to visualize some paradoxical results in the exemplary evaluations of digital websites through an imaginary case description via voting and MCDM. As candidates and voters in SC are put to stand for alternatives and criteria in MCDM, the methodological and pedagogical goals of the study are achieved.

Strong sequences and their consequences in social choice

Jureczko J.

Silesian Journal of Pure and Applied Mathematics

2016

Vol. 6, iss. 1

49--58

One of the most famous theorems in social choice theory – Arrow impossibility theorem – was published in 1951. Since Arrowian paper most researchers tried to ﬁnd diﬀerent versions of this theorem not only for ﬁnite but also for inﬁnite sets of alternative and individuals, where one can treat this situation as anticipation for future social behaviour. The aim of this paper is to ﬁnd some results concerning social voting for inﬁnite sets using one of the combinatorial methods of set theory – strong sequences method. This method was introduced by Eﬁmov in 1965 for proving wellknown theorems in dyadic spaces, (i.e. continuous images of the Cantor cube).

Are we done with preference rankings? if we are, then what?

Nurmi H.

Operations Research and Decisions

2014

Vol. 24, No. 4

63--74

Intransitive, incomplete and discontinuous preferences are not always irrational but may be based on quite reasonable considerations. Hence, we pursue the possibility of building a theory of social choice on an alternative foundation, viz. on individual preference tournaments. Tournaments have been studied for a long time independently of rankings and a number of results are therefore just waiting to be applied in social choice. Our focus is on Slater’s rule. A new interpretation of the rule is provided.

Elementy teorii użyteczności w analizie procesu nauczania

Kołwzan W., Pieronek J.

Zeszyty Naukowe / Wyższa Szkoła Oficerska Wojsk Lądowych im. gen. T. Kościuszki

2011

Nr 4

325-331

W artykule podjęto próbę oceny procesu kształcenia z pozycji teorii użyteczności i teorii społecznego wyboru. Umieszczony on został w kontekście aksjomatyki i pragmatyki. Podkreślona została też rola e-nauczania. Położono także akcent na miary nauczania od strony szeroko rozumianej teorii wartości.

The authors attempt to carry out an analysis of the teaching process from the position of the utility theory and the social choice theory. They also stress the role of the value theory in the analysis of this process. The role of e-learning is also emphasized in the article.