Logical and historical determination of the Arrow and Sen impossibility theorems

General classification of mathematical statements divides them into universal, those of the form xA , and existential ЭxA ones. Common formulations of impossibility theorems of K. J. Arrow and A. K. Sen are represented by the statements of the form "there is no x such that A". Bearing in mind logical equivalence of formulae ¬ЭxA and x¬A, we come to the conclusion that the corpus of impossibility theorems, which appears in the theory of social choice, could make a specific and recognizable subclass of universal statements. In this paper, on the basis of the established logical and methodological criteria, we point to a sequence of extremely significant "impossibility theorems", reaching throughout the history of mathematics to the present days and the famous results of Arrow and Sen in field of mathematical economics. We close with specifying the context which makes it possible to formulate the results of Arrow and Sen accurately, presenting a new direct proof of Sen’s result, with no reliance on the notion of minimal liberalism.

Teorija racionalnog izbora i ovisničko ponašanje

The purpose of this paper is to explore the construct of student satisfaction and analyze its relationship with student loyalty in the context of state and private universities. The rational choice theory assumes that, when deciding whether to consume some goods or not, consumers use analysis in order to estimate the values of individual preference indicators. From this point of view, there are risk and time preferences. The former show aversion to a risk and are expressed through the risk aversion coefficient, while the latter measure the degree of preference for present satisfaction in relation to the same satisfaction in the future. The degree of preference for present satisfaction regarding the same satisfaction in the future is expressed by the time preference rate. Smokers with a low time preference rate and high risk aversion coefficient level can be expected to be successful in cessation. The aim of this paper is to study smokers from the perspective of rational choice theory, in order to detect factors influencing their behavior. The study (investigation) found that the significant factors for smokers’ behavior are: gender, age, education, risk aversion coefficient, and the time preference rate. Analysis of smokers’ behavior, with appropriate limits and qualifications, is a well-developed and highly effective tool for exploring and interpreting reality.Teorija racionalnog izbora pretpostavlja da se pri odlučivanju o konzumaciji ili nekonzumaciji određenih proizvoda potrošači koriste analizom radi procjene vrijednosti individualnih pokazatelja preferencija. Iz te perspektive postoje preferencije vezane uz rizik i vrijeme. Prve pokazuju averziju prema riziku i izražavaju se koeficijentom averzije prema riziku, dok druge mjere stupanj preferencije za sadašnje zadovoljstvo u odnosu prema istom zadovoljstvu u budućnosti. Stupanj preferencije za sadašnje zadovoljstvo u odnosu na isto zadovoljstvo u budućnosti izražen je stopom preferencije vremena. Od pušača koji pokazuju nisku stopu preferencije prema vremenu i visoku stopu razine koeficijenta averzije može se očekivati uspješnost u prestanku pušenja. Cilj je rada proučavanje pušača iz perspektive teorije racionalnog izbora kako bi se otkrili čimbenici koji utječu na njihovo ponašanje. Istraživanjem je ustanovljeno da su značajni čimbenici ponašanja pušača sljedeći: spol, dob, obrazovanje, koeficijent averzije prema riziku i stopa vremenske preferencije. Analiza ponašanja pušača, uz uvažavanje odgovarajućih ograničenja i mogućnosti, dobro je razvijen alat za istraživanje i interpretaciju stvarnosti

Glazbene preferencije studenata: uloga glazbenog obrazovanja, karakteristika glazbe i značajki osobnosti

The aim of this research was to examine the relationship between music education and musical preferences for different tempo and tonality and to explore what personality traits of the Big five-factor model contribute to the explanation of individual differences in musical preferences. The survey included 202 female and male students of the University of Split who were selected on the basis of their music education. Music compact disc containing 16 musical excerpts, Questionnaire for testing musical preference and Questionnaire for personality traits were used. The results confirmed the significant effects of music education and music characteristics on the musical preferences. Participants with the highest degree of music education enjoy all musical examples alike, regardless of musical characteristics, while other participants reported a significantly higher degree of liking the music in major key and fast tempo. Music education was a significant predictor in explaining musical preferences for major key music in fast tempo, while openness to experience was significant in predicting preferences for the minor music in slow tempo.Cilj istraživanja bio je ispitati odnos između glazbenog obrazovanja i preferencija glazbe različitog tempa i tonaliteta te provjeriti koje osobine ličnosti iz petfaktorskog modela doprinose objašnjenju individualnih razlika u glazbenim preferencijama. U istraživanju je sudjelovalo 202 studentica i studenata Sveučilišta u Splitu koji su odabrani na temelju kriterija glazbenog obrazovanja. Za potrebe istraživanja pripremljen je glazbeni nosač zvuka, Upitnik za ispitivanje glazbenih preferencija i Upitnik za ispitivanje osobina ličnosti. Rezultati potvrđuju značajne efekte glazbenog obrazovanja i glazbenih osobina na preferencije glazbe različitog tempa i tonaliteta. Sudionici s najvećim stupnjem glazbenog obrazovanja podjednako preferiraju glazbu bez obzira na njezine karakteristike, a ostali sudionici iskazuju značajno veći stupanj prefiranja durske glazbe brzog tempa. Značajnim prediktorima u objašnjenju glazbenih preferencija pokazalo se glazbeno obrazovanje za dursku glazbu brzog tempa, a osobina intelekta za molsku glazbu polaganog tempa

Preferencije u odabiru rodno tipiziranih i rodno neutralnih igračaka kod djece predškolske dobi

Igračke igraju veliku ulogu u djetinjstvu i potiču razvoj različitih kognitivnih, socijalnih i motoričkih vještina. Smatra se da igračke sadrže ideologije i promoviraju ulogu identiteta društva koje ih proizvodi (Kahlenberg i Hein, 2009). U ovom su se istraživanju ispitivale preferencije rodno tipiziranih igračaka kod djece predškolske dobi. Nakon razgovora s djecom odabrano je 30 igračaka koja su djeca navela kao omiljene. Tih su 30 igračaka zatim djeca procijenjivala kao igračke „za djevojčice“, „za dječake“ ili „za djevojčice i dječake“. Od tih 30 igračaka 3 igračke koje su najviše puta odabrane kao igračke za djevojčice, 3 igračke koje s u najviše puta odabrane za dječake i 3 igračke koje su najviše puta odabrane za djevojčice koristile su se u ispitivanju preferencija rodno tipiziranih i rodno neutralnih igračaka kod djece. Djeca su većinom preferirala rodno tipizirane igračke. Najviše su to činile djevojčice za djevojčice (94.12%), a najmanje dječaci za dječake (71.43%) što nije konzistentno ostaloj literaturi (Biernat, 1991; Berk, 2013; Vasta, Haith i Miller, 2002; Cherney i London, 2006; Karniol i Aida, 1997). Odabrane igračke za djevojčice bile su vezane uz ljepotu i njegu, te pastelnih i ružičastih boja, a za dječake vezane uz uzbuđenje i nasilje, plavih, neonskih i crne boje.Toys play a big role in childhood and they encourage development of different cognitive, social and motor skills. It is considered that toys contain ideologies which promulgate the role identities of the society that creates them. In this research we have questioned preferences of gender-typed toys in preschool children. After the conversations with children we have chosen 30 toys that were liked the most. These 30 toys were then valued by the children, whether they thought the toy was “for boys”, “for girls” or for both. Out of these 30 toys, 3 toys that were chosen “for boys” the most, 3 toys that were chosen “for girls” the most and 3 toys that were chosen “for both” the most, were then used in a survey of preferences of gender-typed toys. Children usually preferred gender-typed toys. Mostly, it was done by girls for girls (94,12%), and leastly boys for boys (71,43%) which is not consistent with the rest of the literature on this subject matter (Biernat, 1991; Berk, 2013; Vasta, Haith i Miller, 2002; Cherney i London, 2006; Karniol i Aida, 1997). Toys chosen for girls were linked with beauty and care, pink and pastel coloured, while the ones for boys were thrill and violence based, coloured mostly in blue, black and neon colours

Imprinting - tipe of learning in birds

Imprint je način učenja koji nastupa kada životinjsku jedinku dok se nalazi u osjetljivom periodu izložimo određenim stimulansima, izazivajući kao reakciju trajne promjene ponašanja. Najprisutnije vrste imprinta su filialni i seksualni imprint. Osjetljivi period u kojem je jedinku moguće imprintati varira zavisno o vrsti životinje i vrsti samog imprinta. Fenomen imprinta prisutan je kod nekih vrsta sisavaca, a posebno kod ptica. Učinci mogu ostati prisutni tokom cijelog života jedinke, ali nisu uvijek potpuno ireverzibilni iako se isprva, u nekim slučajevima mogu doimati takvima. Ireverzibilnost kao i drugi aspekti imprinta, ovisi o vrsti životinje koju se imprinta, trenutku u kojem se imprint odvija, intenzitetu postupka, te mnogim drugim čimbenicima.Imprinting is an individual animal`s learning to respond to a sign stimulus (realeaser) only at a particular time (sensitive period) of it life and often retaining this response throughout its life. The most immanent are the sexual and filial imprinting. The duration, and timing of sensitive periods varies depending on the imprinting species and the nature of the imprinting (sexual, filial...). The phenomenon of imprinting is clearly present in the development of some mamals, and especially birds. The affects of imprinting can be retained throughout entire life of an animal, but they are not completely irreversible. Irreversibility, as well as some other aspects of imprinting, depends on the imprinting species, the time period in which it`s taking place, intensity, and many other factors

Characteristics of imprinting in vertebrates

Imprint je specijalizirani tip učenja koji utječe na trajne, za mnoge autore i nepovratne promjene u ponašanju jedinke. Najbolje je istražen kod ptica, ali se pojavljuje i kod drugih životinja, a glavna mu je komponenta osjetljivi period. Iako se prvotno tvrdilo da je potpuno ireverzibilan, u novijoj literaturi se govori o barem djelomičnoj povratnosti. Osim nepovratnosti i osjetljivog perioda, razliku od uobičajenog učenja čini i sam princip. Naime, životinje se ovdje ne ponašaju po principu pokušaja i pogreške, niti su vođene nagradom i kaznom, već sama izloženost podražaju u određenom vremenu, određuje njihovo buduće ponašanje. Najpoznatiji tipovi imprinta su filialni, koji omogućuje mladom da pozna svoju majku, i seksualni imprint, kojime mlado prepoznaje potencijalne partnere. I jedan i drugi najbolje su istraženi kod različitih ptičjih vrsta, a iako imaju neke zajedničke komponente, ova dva tipa imprinta razlikuju se prvenstveno po vremenu kada nastupa osjetljivi period. Osim toga, dok je karakteristika filialnog imprinta naklonjenost mladunca jedinki koju smatra majkom, kod seksualnog se stvaraju preferencije prema obilježjima vrste, a ne prema određenoj jedinki. Učinci ovog fenomena ovise o mnogim čimbenicima, kao što su vrsta životinje, vrijeme i duljina trajanja izlaganja određenom stimulansu, pa čak i spol kod pojedinih vrsta. Unatoč svemu tome, imprint je u mnogo slučajevima nepovratno učenje, kao što se to od samog otkrića tvrdilo, a za potpuno razumijevanje potrebno je još mnogo istraživanja.Imprint is a specialized type of learning that affects permanent, and according to many authors, irreversible changes in the behavior of individuals. It is best explored in birds, even though it occurs in other animals as well, and main component of this phenomenon is the sensitive period. Although it was initially claimed that it was irreversible, the recent literature claims there is at least partial reversibility. Besides irreversibility and the sensitive period, principle of learning also makes a difference between imprint and typical learning. In the case of imprint, animals do not behave according to the principle of trial and error, and are not guided by rewards and punishments; rather, the very exposure to stimuli in a given time determines their future behavior. Filial imprinting, which allows a young to know its mother, and sexual, which enables it to recognize potential partners, are the two best-known types of imprinting. Both types are best explored in various bird species, and although they have some common characteristics, these two types of imprinting differ primarily with regard to the time when sensitive period appears. In addition, while the characteristic of filial imprinting is preferring individual that is considered to be its mother, in sexual imprinting, the animal creates preferences for features of species, and not particular individuals. The effects of this phenomenon depend on many factors, such as species, time and duration of exposure to a particular stimulus, and in some species even gender. However, the imprinting is in many cases irreversible, as it is claimed in history of research, and complete understanding of it requires a lot of research

Behavioral welfare economics

This paper discusses several competing proposals for general normative frameworks thatwould encompass non-standard models of choice. Most existing proposals equate welfare with wellbeing. Some assume that well-being flows from the achievement of well-defined objectives, and that those objectives also guide choices; the trick is to formulate a framework in which less-than-completely coherent choice patterns reveal the unobserved objectives. Others are predicated on the contention that well-being, and hence welfare, is directly measurable. Both of those approaches encounter serious conceptual difficulties. An alternative approach, developed by Bernheim and Rangel (2009), defines welfare directly in terms of choice. It entails a generalized welfare criterion that respects choice directly, without requiring any rationalization involving potentially unverifiable assumptions concerning underlying objectives and their relationships to choice. Because useful behavioral theories generally envision a substatial degree of underlying coherence in behavior, that criterion leads to a rich and tractable normative framework.Modeli izbora, Blagostanje, Preferencije.

Behavioral welfare economics

This paper discusses several competing proposals for general normative frameworks thatwould encompass non-standard models of choice. Most existing proposals equate welfare with wellbeing. Some assume that well-being flows from the achievement of well-defined objectives, and that those objectives also guide choices; the trick is to formulate a framework in which less-than-completely coherent choice patterns reveal the unobserved objectives. Others are predicated on the contention that well-being, and hence welfare, is directly measurable. Both of those approaches encounter serious conceptual difficulties. An alternative approach, developed by Bernheim and Rangel (2009), defines welfare directly in terms of choice. It entails a generalized welfare criterion that respects choice directly, without requiring any rationalization involving potentially unverifiable assumptions concerning underlying objectives and their relationships to choice. Because useful behavioral theories generally envision a substatial degree of underlying coherence in behavior, that criterion leads to a rich and tractable normative framework.The models of choice, Welfare, Preferences.

Pregovaranje

U ovom radu obrađena je tema pregovaranje i kooperativnih igara. Za to je potrebno razumijevanje osnovnih pojmova iz teorije korisnosti i poznavanje najvažnijih rezultata. To podrazumijeva von Neumannov i Morgensternov teorem koji daje postojanje funkcije korisnosti koja čuva preferencije donositelja odluke, ali mora zadovoljavati slabi uređaj, netrivijalnost, redukciju, supstituciju, monotonost i neprekidnost. Također, važno je i da je dobivena korisnost jedinstvena do na pozitivnu afinu transformaciju. Ta dva rezultat nisu dokazana u ovome radu, jer su dokazi dani na predavanjima. Glavni dio ovoga rada predstavljaju Nashovi rezultati iz područja pregovaranja. Detaljno je dokazan Nashov teorem koji daje jedinstveno rješenje problema pregovaranja kao argument maksimuma umnoška funkcija korisnosti, uz uvjet da su zadovoljeni aksiomi invarijantnosti, simetrije, nezavisnosti i Paretov aksiom. Svaki od tih aksioma je obrađen i obrazložen, te je dan primjer za svaki aksiom koji pokazuje da su svi aksiomi nužni i da se niti jedan ne može ublažiti. Nashovo rješenje je prikazano i obrazloženo i grafički radi lakšeg razumijevanja. Osnovni primjer u radu je ”Dilema zatvorenika”. Na vrlo životnom primjeru je pokazan paradoks igranja isključivo u svrhu ostvarivanja vlastite maksimalne korisnosti. Isto se može vidjeti i na primjeru dva trgovca koji oba žele maksimizirati svoj profit, ali i izbaciti drugog trgovca iz posla; ili na primjeru dvije velesile koje odlučuju o razini naoružanja, što se moglo vidjet i kroz povijest na primjeru SAD-a i SSSR-a. Utrka u naoružanju završila je tek kada je SSSR ostao bez novčanih sredstava, a sve to zbog izostanka kooperacije. To mi je dalo motiv da dođem do poopćenja Nashove teorije. ”Dilema zatvorenika” poslužila je kao pomoć pri dobivanju osnovne ideje koja se kasnije poopćila. Dano je prvo razrješenjeˇ ”Dileme zatvorenika” i detaljno objašnjeno kako bi igrači trebali igrati da bi ostvarili ukupnu maksimalnu korisnost. Također, na tom primjeru je utvrđeno da možemo promatrati zbroj funkcija korisnosti, što je često jednostavnije od umnoška, i dobiti rješenje identično Nashovom. To je bila motivacija da se isti rezultat pokaže i u općenitom slučaju, uz pretpostavku da je funkcija dobivena zbrajanjem funkcija korisnosti strogo monotona. U zadnjem poglavlju promatra se Kalai-Smorodinsky rješenje problema pregovaranja. Dokazan je teorem koji daj nužne i dovoljne uvjete za postojanje Kalai-Smorodinsky rješenja. Zahtjeva se zadovoljavanje aksioma invarijantnosti, simetrije, homogene idealne nezavisnosti i netrivijalnosti. Taj je rezultat također dokazan. Dodatno, obrađen je i primjer koji daje usporedbu Kalai-Smorodinsky i Nashovog rješenja, te pokazuje da postoje i drugi načini rješavanja problema pregovaranja, npr. računanjem Walrasovog ekvilibrija.In this these we are studying bargaining and cooperative games. In order to understand that, we should be familiar with the basic terms of the utility theory of von Neumann and Morgenstern, based on the axioms on the page 8. They are weak condition, non-triviality, reduction, substitution, monotony and continuity. Proofs of those two results are not given in this paper, since they were given in class. The main part in this study is given by Nash: The Barganing Problem, Econometrica 18 (1950), 155-162 and Two-Person Cooperative Games, Econometrica 21 (1953), br. 1 , 128-140. Nash’s axioms provides a unique solution to the negotiation problem as an argument of the maximum product of the utility function, if the axioms of invariance, symmetry, independence and Pareto axiom are satisfied. Each of these axioms is processed and reasoned, and the example is given for every axiom that shows that all axioms are necessary and that none can be mitigated. Nash’s solution is illustrated and explained also graphically so it is more convenient to understand it. The main example in the paper is ”Prisoner’s Dilemma”. The example shows the paradox of playing solely for the purpose of achieving the maximum utility for yourself. The same can be seen in the example of two traders who both want to maximize their profits, but also throw another trader out of business; or the example of two great powers that have the power to decide the quantity of the armaments, which is shown through the history with the example of the USA and the USSR. The arms race ended when the USSR was left without funds, because of a lack of cooperation. This gave me the motivation to get to generalizations of the Nash theory. ” Prisoner’s Dilemma ” served as assistance in obtaining basic ideas which were later generalized. It is given the dismissal of ” Prisoner’s Dilemma” and it was precisely explained how the players should play in order to reach the highest total maximum utility. Also, in this example it is found that we can observe the sum of the utility function, which is often more simple than the product, and get a solution identical to Nash’s. This was the motivation to show the same result in the general case, with the premise that the function is obtained by summing the utility function as strictly monotone. The final chapter discusses the Kalai-Smorodinsky bargaining solution to the problem. The theorem which gives the necessary and su fficient conditions for the existence of Kalai-Smorodinsky solution is proved. Those conditiones are the axioms of scale invariance, symmetry, homogeneous ideal independence of irrelevant alternatives and non-triviality. In addition, an example that provides a comparison of Kalai-Smorodinsky and Nash bargaining solutions was processed and it shows that there are other ways of solving the problem of bargaining, such as calculating Walras equilibrium

Elementary school students' preferences for musical activities

Ovaj diplomski rad namijenjen je istraživanju sklonosti učenika nižih razreda osnovne škole prema glazbenim aktivnostima. Govoriti će se o nastavi Glazbene kulture u osnovnoj školi glazbenim aktivnostima koje se provode tokom nastave Glazbene kulture u osnovnoj školi o glazbenim aktivnostima koje učitelji najčešće provode te jesu li one u skladu s učeničkim preferencijama. Naglasak će se staviti na glazbene aktivnosti koje učenici preferiraju te će se provjeriti postoji li razlika u njihovim preferencijama s obzirom na dob učenika, odnosno na razred koji pohađaju. Zbog pretpostavke da učitelji i dalje u nastavi Glazbene kulture najčešće provode glazbene aktivnosti pjevanja u ovom istraživanju provjeriti ćemo jesu li to aktivnosti koje i učenici najviše preferiraju i postoji li promjena u preferencijama učenika s obzirom na njihovu dob, a u koju bi učitelji trebali biti upućeni da bi mogli promijeniti nastavnu praksu kako bi ona bila u skladu s potrebama učenika. Istraživanje je provedeno tijekom lipnja 2019. godine u Osnovnoj školi Frane Krste Frankopana u Osijeku na uzorku od 113 učenika od prvog do trećeg razreda te su uzeta po dva razredna odjela od svakog razreda. U istraživanju je primijenjen anketni upitnik i skala procjene za ispitivanje preferencija prema pojedinim glazbenim aktivnostima. Nadalje, ispitalo se koje se glazbene aktivnosti najčešće provode, a koje bi učenici voljeli da češće budu dio nastave Glazbene kulture. Rezultati istraživanja pokazuju da je najpreferiranija glazbena aktivnost glazbene igre, a najmanje preferirana glazbena aktivnost glazbeno stvaralaštvo. Utvrđeno je da učitelji najčešće provode pjevanje u nastavi Glazbene kulture što nije u skladu s učeničkim preferencijama.The aim of the research was to investigate music preferences of pupils in the lower grades of primary school in musical activities. We will be talking about Music classes in general, about musical activities conducted in teaching Music in primary school and about musical activities which are most often used by primary school teachers. We will also check if there is a connection between musical activities that are preferred by pupils and musical activities that teachers most often use. Also, the research wanted to examine the influence of grade level on pupils’ preferences. Because of assumption that singing is the most used musical activity by teachers we will check if singing is the most preferred musical activity by pupils, and if there is any change in musical activity preferences by pupils that teachers need to know in order to be able to change their teaching to be in tune with the pupils’ needs. The research was conducted in primary school Frana Krste Frankopana in Osijek during June of 2019. The sample included 113 pupils in grades one to three. In order to collect data in this research we used a questionnaire with an evaluation scale intended to measure preferences for musical activities. Moreover, we examined which musical activities are the most commonly used by teachers and which musical activities would pupils prefer to be included more often. The results show that the most preferred musical activity is musical games, and the least preferred musical activity is musical creation. It has been established that in musical classes teachers use singing most often which is not compatible with pupils’ preferences