10 research outputs found
An operator view on alliances in politics
We introduce the concept of an {\em operator decision making technique} and
apply it to a concrete political problem: should a given political party form a
coalition or not? We focus on the situation of three political parties, and
divide the electorate into four groups: partisan supporters of each party and a
group of undecided voters. We consider party-party interactions of two forms:
shared or differing alliance attitudes. Our main results consist of
time-dependent decision functions for each of the three parties, and their
asymptotic values, i.e., their final decisions on whether or not to form a
coalition.Comment: In press in SIAM J. of Applied Mathematic
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Quantum like modelling of decision making: quantifying uncertainty with the aid of the Heisenberg-Robertson inequality
This paper contributes to quantum-like modeling of decision making (DM) under uncertainty through application of Heisenbergâs uncertainty principle (in the form of the Robertson inequality). In this paper we apply this instrument to quantify uncertainty in DM performed by quantum-like agents. As an example, we apply the Heisenberg uncertainty principle to the determination of mutual interrelation of uncertainties for âincompatible questionsâ used to be asked in political opinion pools. We also consider the problem of representation of decision problems, e.g., in the form of questions, by Hermitian operators, commuting and noncommuting, corresponding to compatible and incompatible questions respectively. Our construction unifies the two different situations (compatible versus incompatible mental observables), by means of a single Hilbert space and of a deformation parameter which can be tuned to describe these opposite cases. One of the main foundational consequences of this paper for cognitive psychology is formalization of the mutual uncertainty about incompatible questions with the aid of Heisenbergâs uncertainty principle implying the mental state dependence of (in)compatibility of questions
First results on applying a non-linear effect formalism to alliances between political parties and buy and sell dynamics
We discuss a non linear extension of a model of alliances in politics,
recently proposed by one of us. The model is constructed in terms of operators,
describing the \emph{interest} of three parties to form, or not, some political
alliance with the other parties. The time evolution of what we call \emph{the
decision functions} is deduced by introducing a suitable hamiltonian, which
describes the main effects of the interactions of the parties amongst
themselves and with their \emph{environments}, {which are }generated by their
electors and by people who still have no clear {idea }for which party to vote
(or even if to vote). The hamiltonian contains some non-linear effects, which
takes into account the role of a party in the decision process of the other two
parties. Moreover, we show how the same hamiltonian can also be used to
construct a formal structure which can describe the dynamics of buying and
selling financial assets (without however implying a specific price setting
mechanism).Comment: arXiv admin note: text overlap with arXiv:1502.0173
A model of adaptive decision making from representation of information environment by quantum fields
We present the mathematical model of decision making (DM) of agents acting in
a complex and uncertain environment (combining huge variety of economical,
financial, behavioral, and geo-political factors). To describe interaction of
agents with it, we apply the formalism of quantum field theory (QTF). Quantum
fields are of the purely informational nature. The QFT-model can be treated as
a far relative of the expected utility theory, where the role of utility is
played by adaptivity to an environment (bath). However, this sort of
utility-adaptivity cannot be represented simply as a numerical function. The
operator representation in Hilbert space is used and adaptivity is described as
in quantum dynamics. We are especially interested in stabilization of solutions
for sufficiently large time. The outputs of this stabilization process,
probabilities for possible choices, are treated in the framework of classical
DM. To connect classical and quantum DM, we appeal to Quantum Bayesianism
(QBism). We demonstrate the quantum-like interference effect in DM which is
exhibited as a violation of the formula of total probability and hence the
classical Bayesian inference scheme.Comment: in press in Philosophical Transactions
Quantum field inspired model of decision making: Asymptotic stabilization of belief state via interaction with surrounding mental environment
This paper is devoted to justification of the quantum-like model of the process of decision making based on theory of open quantum systems: decision making as decoher- ence. This process is modeled as interaction of a decision maker, Alice, with a mental (information) environment R surrounding her. Such an interaction generates âdissipation of uncertaintyâ from Aliceâs belief-state Ï ( t ) into R and asymptotic stabilization of Ï ( t ) to a steady belief-state. The latter is treated as the decision state. Mathematically the problem under study is about finding constraints on R guaranteeing such stabilization. We found a partial solution of this problem (in the form of sufficient conditions). We present the corresponding decision making analysis for one class of mental environments, so-called âalmost homogeneous environmentsâ, with the illustrative examples: a) behavior of electorate interacting with the mass-media âreservoirâ; b) consumersâ persuasion. We also comment on other classes of mental environments
Modeling interactions between political parties and electors
In this paper we extend some recent results on an operatorial approach to the
description of alliances between political parties interacting among themselves
and with a basin of electors. In particular, we propose and compare three
different models, deducing the dynamics of their related {\em decision
functions}, i.e. the attitude of each party to form or not an alliance. In the
first model the interactions between each party and their electors are
considered. We show that these interactions drive the decision functions
towards certain asymptotic values depending on the electors only: this is the
{\em perfect party}, which behaves following the electors' suggestions. The
second model is an extension of the first one in which we include a
which modifies the status of the electors, and of the decision functions as a
consequence, at some specific time step. In the third model we neglect the
interactions with the electors while we consider cubic and quartic interactions
between the parties and we show that we get (slightly oscillating) asymptotic
values for the decision functions, close to their initial values. This is the
{\em real party}, which does not listen to the electors. Several explicit
situations are considered in details and numerical results are also shown.Comment: To appear in Physica
Dynamics for a quantum parliament
In this paper we propose a dynamical approach based on the
Gorini-Kossakowski-Sudarshan-Lindblad equation for a problem of decision
making. More specifically, we consider what was recently called a quantum
parliament, asked to approve or not a certain law, and we propose a model of
the connections between the various members of the parliament, proposing in
particular some special form of the interactions giving rise to a {\em
collaborative} or non collaborative behaviour