Современные избирательные технологии : использование математических методов передачи голосов избирателей
We propose a new method for conducting Single transferable vote (STV) elections and provide a unified method for describing classic STV procedures (the Gregory Method, the inclusive Gregory method and the Weighted inclusive Gregory method) as an iterative procedure. We also propose a modification for quota definition that improves the theoretical properties of the procedures. The method is justified by utilising a new set of axioms. We show that this method extends the Weighted inclusive Gregory method with the modified definition of quota and random equiprobable selection of a winning coalition in each iteration. The results are extended to the methods, allowing fractional numbers of votes.
A general description in the form of an iterative procedure of methods implementing the Single Transferable Vote (STV) is given. Woodall's axiomatics for ordinal proportional representation systems is examined. New axioms for STV are constructed with modification of quota. The new definition of quota improves the theoretical properties of the procedure. A new method is proposed based on STV and the new definition of the quota. A theorem is proved that this method is the only one satisfying these axioms. This method called the weighted inclusive Gregory method with modified quota and random equiprobable choice of the winning coalition on each iteration. Results are extended to the methods that transfer a fractional number of votes.
We consider certain spaces of functions on the circle, which naturally appear in harmonic analysis, and superposition operators on these spaces. We study the following question: which functions have the property that each their superposition with a homeomorphism of the circle belongs to a given space? We also study the multidimensional case.
We consider the spaces of functions on the m-dimensional torus, whose Fourier transform is p -summable. We obtain estimates for the norms of the exponential functions deformed by a C1 -smooth phase. The results generalize to the multidimensional case the one-dimensional results obtained by the author earlier in “Quantitative estimates in the Beurling—Helson theorem”, Sbornik: Mathematics, 201:12 (2010), 1811 – 1836.
We consider the spaces of function on the circle whose Fourier transform is p-summable. We obtain estimates for the norms of exponential functions deformed by a C1 -smooth phase.