scholarly journals Revisiting the Approximation Bound for Stochastic Submodular Cover

2018 ◽  
Vol 63 ◽  
pp. 265-279
Author(s):  
Lisa Hellerstein ◽  
Devorah Kletenik

Deshpande et al. presented a k(ln R + 1) approximation bound for Stochastic Submodular Cover, where k is the state set size, R is the maximum utility of a single item, and the utility function is integer-valued. This bound is similar to the ln Q/(eta+1) bound given by Golovin and Krause, whose analysis was recently found to have an error. Here Q >= R is the goal utility and eta is the minimum gap between Q and any attainable utility Q' < Q. We revisit the proof of the k(ln R + 1) bound of Deshpande et al., fill in the details of the proof of a key lemma, and prove two bounds for real-valued utility functions: k(ln R_1 + 1) and (ln R_E + 1). Here R_1 equals the maximum ratio between the largest increase in utility attainable from a single item, and the smallest non-zero increase attainable from that same item (in the same state). The quantity R_E equals the maximum ratio between the largest expected increase in utility from a single item, and the smallest non-zero expected increase in utility from that same item. Our bounds apply only to the stochastic setting with independent states.

Politeia ◽  
2018 ◽  
Vol 37 (1) ◽  
Author(s):  
Pamela Johnson

As members of the secret Afrikaner organisation, the Broederbond, two of the apartheid-era rectors at the University of Fort Hare were responsible for leading an institution that was supposed to spearhead the modernisation of ethnically defined homelands and their transition to independent states, whilst disseminating apartheid values among the black students. Based on unsorted and unarchived documents located in the personal files of the apartheid-era rectors, which included secret correspondence and memoranda of clandestine meetings, this paper illustrates the attempted exercise of hegemony by the apartheid state through its linked network with the university administration during the period 1960 to 1990. This is achieved by demonstrating the interaction between the state, Broederbond rectors and the black students at Fort Hare, who were subjected to persuasion and coercion as dictated by the state’s apartheid vision of a racially defined and separated society.


2020 ◽  
Vol 22 (5) ◽  
pp. 98-118
Author(s):  
ALYM K. ANNAMURADOV ◽  
◽  
OVEZDURDY B. MUKHAMMETBERDIEV ◽  
MURAD O. HAITOV ◽  
◽  
...  

The article examines the formation of the statehood of modern Turkmenistan through the prism of historical changes that have occurred in the post-Soviet countries. It is noted that after 1991 all former republics of the USSR built new independent states on a fundamentally different basis – interaction between government and society. The authors emphasize that the establishment of trust between the state as an institution and citizens is possible under certain conditions, among which a special place is occupied by a clear organization of civil service and the professionalism of civil servants. The measures that have already been implemented and are being taken by the leadership of Turkmenistan at the present time to solve these problems are considered. It is noted that Turkmenistan acts within the framework and in accordance with the key world-class standards regarding the requirements for the organization of civil service. The measures taken in the country to combat corruption are analyzed.


2014 ◽  
Vol 17 (03) ◽  
pp. 1450018 ◽  
Author(s):  
ALEXANDER M. G. COX ◽  
DAVID HOBSON ◽  
JAN OBłÓJ

We pursue an inverse approach to utility theory and associated consumption and investment problems. Instead of specifying a utility function and deriving the actions of an agent, we assume that we observe the actions of the agent (i.e. consumption and investment strategies) and ask if it is possible to derive a utility function for which the observed behavior is optimal. We work in continuous time both in a deterministic and stochastic setting. In the deterministic setup, we find that there are infinitely many utility functions generating a given consumption pattern. In the stochastic setting of a geometric Brownian motion market it turns out that the consumption and investment strategies have to satisfy a consistency condition (PDE) if they are to come from a classical utility maximization problem. We show further that important characteristics of the agent such as risk attitudes (e.g., DARA) can be deduced directly from the agent's consumption and investment choices.


2020 ◽  
Author(s):  
Hui Song ◽  
Yongshun Wang ◽  
Peng Hong ◽  
Linsen Chen

Author(s):  
ARON LARSSON ◽  
JIM JOHANSSON ◽  
LOVE EKENBERG ◽  
MATS DANIELSON

We present a decision tree evaluation method for analyzing multi-attribute decisions under risk, where information is numerically imprecise. The approach extends the use of additive and multiplicative utility functions for supporting evaluation of imprecise statements, relaxing requirements for precise estimates of decision parameters. Information is modeled in convex sets of utility and probability measures restricted by closed intervals. Evaluation is done relative to a set of rules, generalizing the concept of admissibility, computationally handled through optimization of aggregated utility functions. Pros and cons of two approaches, and tradeoffs in selecting a utility function, are discussed.


2021 ◽  
Author(s):  
Philipe M. Bujold ◽  
Simone Ferrari-Toniolo ◽  
Leo Chi U Seak ◽  
Wolfram Schultz

AbstractDecisions can be risky or riskless, depending on the outcomes of the choice. Expected Utility Theory describes risky choices as a utility maximization process: we choose the option with the highest subjective value (utility), which we compute considering both the option’s value and its associated risk. According to the random utility maximization framework, riskless choices could also be based on a utility measure. Neuronal mechanisms of utility-based choice may thus be common to both risky and riskless choices. This assumption would require the existence of a utility function that accounts for both risky and riskless decisions. Here, we investigated whether the choice behavior of macaque monkeys in riskless and risky decisions could be described by a common underlying utility function. We found that the utility functions elicited in the two choice scenarios were different from each other, even after taking into account the contribution of subjective probability weighting. Our results suggest that distinct utility representations exist for riskless and risky choices, which could reflect distinct neuronal representations of the utility quantities, or distinct brain mechanisms for risky and riskless choices. The different utility functions should be taken into account in neuronal investigations of utility-based choice.


2019 ◽  
Vol 3 (1) ◽  
pp. 78
Author(s):  
Dardan Vuniqi

State is society’s need for the existence of an organized power, equipped with the right equipments of coercion and able to run the society, by imposing the choices that seem reasonable to them, through legal norms. State is an organization of state power; it is an organized power which imposes its will to all the society and has a whole mechanism to execute this will. The state realizes its functions through power, which is a mechanism to accomplish its relevant functions. The power’s concept is a social concept, which can be understood only as a relation between two subjects, between two wills. Power is the ability to impose an order, a rule and other’s behavior in case that he doesn’t apply voluntary the relevant norm, respectively the right. Using state power is related to creation and application, respectively the implementation of law. To understand state power better, we have to start from its overall character. So, we notice that in practice we encounter different kinds of powers: the family’s one, the school’s one, the health’s one, the religion’s, culture’s etc. The notion of powers can be understood as a report between two subjects, two wills. Power is an order for other’s behavior. Every power is some kind of liability, dependence from others. In the legal aspect, supremacy of state presents the constitutive – legislative form upon the powers that follow after it. Supremacy, respectively the prevalence, is stronger upon other powers in its territory. For example we take the highest state body, the parliament as a legislative body, where all other powers that come after it, like the executive and court’s one, are dependable on state’s central power. We can’t avoid the carriage of state’s sovereignty in the competences of different international organizations. Republic, based on ratified agreements for certain cases can overstep state’s power on international organizations. The people legitimate power and its bodies, by giving their votes for a mandate of governance (people’s verdict). It is true that we understand people’s sovereignty only as a quality of people, where with the word people we understand the entirety of citizens that live in a state. The sovereignty’s case actualizes especially to prove people’s right for self-determination until the disconnection that can be seen as national – state sovereignty. National sovereignty is the right of a nation for self-determination. Sovereignty’s cease happens when the monopoly of physical strength ceases as well, and this monopoly is won by another organization. A state can be ceased with the voluntary union of two or more states in a mutual state, or a state can be ceased from a federative state, where federal units win their independence. In this context we have to do with former USSR’s units, separated in some independent states, like Czechoslovakia unit that was separated in two independent states: in Czech Republic and Slovakia. Former Yugoslavia was separated from eight federal units, today from these federal units seven of them have won their independence and their international recognition, and the Republic of Kosovo is one amongst them. Every state power’s activity has legal effect inside the borders of a certain territory and inside this territory the people come under the relevant state’s power. Territorial expansion of state power is three dimensional. The first dimension includes the land inside a state’s borders, the second dimension includes the airspace upon the land and the third dimension includes water space. The airspace upon inside territorial waters is also a power upon people and the power is not universal, meaning that it doesn’t include all mankind. State territory is the space that’s under state’s sovereignty. It is an essential element for its existence. According to the author Juaraj Andrassy, state territory lies in land and water space inside the borders, land and water under this space and the air upon it. Coastal waters and air are considered as parts that belong to land area, because in every case they share her destiny. Exceptionally, according to the international right or international treaties, it is possible that in one certain state’s territory another state’s power can be used. In this case we have to do with the extraterritoriality of state power. The state extraterritoriality’s institute is connected to the concept of another state’s territory, where we have to do with diplomatic representatives of a foreign country, where in the buildings of these diplomatic representatives, the power of the current state is not used. These buildings, according to the international right, the diplomatic right, have territorial immunity and the relevant host state bodies don’t have any power. Regarding to inviolability, respectively within this case, we have two groups to mention: the real immunity and the personal immunity, which are connected with the extraterritoriality’s institute. Key words: Independence, Sovereignty, Preponderance, Prevalence, Territorial Expansion.


Metamorphosis ◽  
2014 ◽  
Vol 13 (1) ◽  
pp. 26-32
Author(s):  
Afreen Arif H. ◽  
T.P.M. Pakkala

Most of the utility functions studied earlier concentrated on properties of risk aversion. In this article, the authors have introduced a new class of utility function called the Power Law with Exponential Cut-off (PLEC) utility function, which exhibits all the absolute and relative risk aversion and risk loving preferences of individuals, under various conditions. It generalises and encompasses other systems of utility functions like that of exponential power. Certain properties of this utility function are discussed. Sensitivity analysis exhibits different portfolio allocations for various risk preferences. The analysis also shows that arbitrary risk preferences may lead to biased risk response estimates. Performance of PLEC utility function in portfolio allocation problem is demonstrated through numerical examples. This is evaluated through optimal solutions.


2007 ◽  
Vol 129 (5) ◽  
pp. 584-596 ◽  
Author(s):  
Gürdal Arslan ◽  
Jason R. Marden ◽  
Jeff S. Shamma

We consider an autonomous vehicle-target assignment problem where a group of vehicles are expected to optimally assign themselves to a set of targets. We introduce a game-theoretical formulation of the problem in which the vehicles are viewed as self-interested decision makers. Thus, we seek the optimization of a global utility function through autonomous vehicles that are capable of making individually rational decisions to optimize their own utility functions. The first important aspect of the problem is to choose the utility functions of the vehicles in such a way that the objectives of the vehicles are localized to each vehicle yet aligned with a global utility function. The second important aspect of the problem is to equip the vehicles with an appropriate negotiation mechanism by which each vehicle pursues the optimization of its own utility function. We present several design procedures and accompanying caveats for vehicle utility design. We present two new negotiation mechanisms, namely, “generalized regret monitoring with fading memory and inertia” and “selective spatial adaptive play,” and provide accompanying proofs of their convergence. Finally, we present simulations that illustrate how vehicle negotiations can consistently lead to near-optimal assignments provided that the utilities of the vehicles are designed appropriately.


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