Electoral geometry

U radu je prikaza tematika izborne geometrije, te određene metode krojenja granica izbornih jedinica u svrhu manipuliranja izbornih rezultata. Na jednostavnim primjerima vidjeli smo kako granice izbornih jedinica mogu uvelike promijeniti rezultate izbora iako je broj glasača ostao nepromijenjen. Razradu mjera započeli smo određenim intuitivnim i smislenim pretpostavkama o izbornim jedinicama. Pridržavajući se tih pretpostavki prilikom krojenja granica izbornih jedinica, uvedenim mjerama pokušali smo utvrditi do koje razine je došlo do pristranog krojenja granica. Uveli smo mjere kompaktnosti i konveksnosti područja koje opisuju oblik područja izbornih jedinica, te smo ih dodatno modificirali kako ne bismo kažnjavali ”čudne” granice izbornih jedinica ukoliko su one prouzrokovane granicama države ili obalom. Osim samog oblika područja, raspodjela glasačke populacije unutar same izborne jedinice također igra veliku ulogu u rezultatima izbora, stoga se određene nepravilnosti granica mogu zanemariti ukoliko one obuhvaćaju rjeđe naseljena područja, a dodatno kazniti ukoliko obuhvaćaju gušće naseljena područja. Iako postoji mnoštvo mjera vezanih uz ovu tematiku, niti jedna od njih nije apsolutno objektivna mjera koja nam govori jesu li određene granice pristrano skrojene ili ne. Svaka mjera sama za sebe nije dobar kriterij s obzirom da dvije izborne jedinice mogu dobiti različito rangirane rezultate ovisno o mjeri koju koristimo, stoga da bismo dobili jasniju sliku u obzir moramo uzeti više mjera. Danas je izborna geometrija još uvijek aktualna politička tema, a razni matematički timovi pokušavaju doći do novih mjera i algoritama koji bi pomogli pri rješavanju ove problematike.In this paper, we present the topic of electoral geometry and certain methods of drawing boundaries of the electoral districts in order to manipulate electoral results. Through simple examples, we have seen how district boundaries can change election results even though the number of voters has remained unchanged. We started the elaboration of measures with certain intuitive and meaningful assumptions about electoral districts. Adhering to these assumptions when shaping the boundaries of the electoral districts, with the introduced measures we tried to determine the level to which the bias occurred in drawing the boundaries. We have introduced measures of compactness and convexity of the areas which describe the shape of the electoral districts, and we modified them so as not to penalize “weird” district borders if they are caused by state borders or by coastline. Apart from the shape of the area itself, the distribution of the voting population within the district itself also plays a big role in election results, hence certain irregularities in borders can be neglected if they include sparsely populated areas, and additionally punished if they include more densely populated areas. Although there are many measures related to this topic, none of them is an absolute objective measure that tells us whether certain boundaries are biased drawn or not. None of the measures alone is a good criterion given that two districts can have differently ranked results depending on the measure we use, so to get clearer picture we need to take several measures into account. Electoral geometry is still relevant political topic and various mathematical teams are trying to come up with new measures and algorithms which would help solve this problem