Thu. Jun 1st, 2023

The mathematical theory that allows us to choose the ideal parliament

There is a mathematical theory that would allow the election of members of parliament in a natural way that reflects the preferences of voters. Thanks to an analogous formula, it is possible to choose the movies shown on airplanes – so that every passenger can find something for himself or herself.

This method can rót also find application in competitions, such as the Popularizer of Science, where the spród many candidatesów a group of the best is chosen, and only from it the jury selects the winner. The mathematical formula mentioned is the so-called. elections committeeów.

– The committee can be understood as a group of osób selected on the basis of voter preferencesów – móThe project combines theoretical considerations with the construction of specific algorithms. Eng. Piotr Faliszewski of the Academy of GóUniversity of Science and Technology. A computer scientist from the AGH Department of Computer Science, Electronics and Telecommunications is developing a class systemóIn electoral: points systemóin electing a committeeów. The three-year project received a grant from the OPUS program of the National Science Center.

As Dr. Faliszewski explains, the most natural association with the mechanism of electing this group is, for example, the. election of deputiesóin parliament or the election of electorsóin universities, whichóers then – at the next stage – make their choice of rector. This could also be a municipal council election.

The computer scientist points out that when a large number of candidates are running in electionsów, then such a group is very difficult to assess. And yet it is necessary to create "królist" – or "committee" – group of personsób selected for specific characteristics preferred by votersów, którą can be assessed more accurately. Only póThen people from this group are awarded a function, position or (if it is a competition) – a prize.

– We assume that voters are able to rank candidatesów from the best to the least valued by them. On this basis, we make choicesów – mówi dr hab. Faliszewski.

Rós different applications

This is the principle that can be applied to solve róof different tasks, e.g. findings of a set of filmów to the aircraft’s entertainment system on the transatlantic route – so that every passenger can find something to his liking. – The number of elected films is not importantów are selected in proportion to the number of passengers who value themów. All that matters is that everyone finds something for themselves – mówi scientist.

The mathematical language he created allows to describe methods of election, depending on what parameters are chosen.

– We specify that we want solutions with certain properties, so, for example, we are looking for a candidateów to the parliament possibly ródifferent from each other, but as best as possible from the point of view of society. Or candidateóin the best possible for the largest group of votersów, although perhaps less valued from the point of view of minorities. It all depends on what features the parliament to be formed is to have,” the researcher explains.

Dr. Faliszewski’s project combines theoretical considerations with the construction of specific algorithmsów i programóin computer. In the future, using these tools, companies will be able to solve problems concerning the scope of electionsóin the market and strategic, competitionóin, evaluating groups of people or selecting productsów.