Some Thoughts on MCDM: Myths and Ideas
Decision making is a most important function and process of management. It is one of the most pervasive problems of management and a pervasive problem in general. Multiple criteria decision making is an approach to decision making. It is the making of decisions taking into consideration multiple conflicting objectives. How do we make decisions? What is involved? There are many simple paradigms, and until recently about all that could be said was that you should list the alternatives, score them on certain dimensions, and then somehow aggregate the scores, and choose an alternative. Unfortunately, many excellent decision makers simply choose an alternative, based on instinct, intuition, or feel. Then they go on. Though that is fine in many cases; in some cases it is not. In this paper I consider some myths of decision making. I then propose some steps that we, as decision analysts and scientists, should consider taking to try to sensitize decision makers to thinking more about their decisions and making better decisions.
Approximation method for computationally expensive nonconvex multiobjective optimization problems
Haanpaa, Tomi Approximation Method for Computationally Expensive Nonconvex Multiobjective Optimization Problems Jyvaskyla: University of Jyvaskyla, 2012, 180 p. (Jyvaskyla Studies in Computing ISSN 1456-5390; 157) ISBN 978-951-39-4967-9 (nid.) ISBN 978-951-39-4968-6 (PDF) Finnish summary Diss. The importance of optimization for decision makers solving real-life engineering problems has increased in recent decades. In the literature, methods created for multiobjective optimization problems are typically directed for problems where objective function values can be calculated fast. If function evaluations are computationally expensive, i.e. time-consuming, then only fewmethods are available and, usually, they involve assumptions like convex objective functions. To be able to solve more demanding multiobjective optimization problems in future, both the nonconvexity and the computational cost of the problem in question must be considered. In this thesis, an approximation method, Interactive HyperBox Exploration (IHBE), is proposed for computationally expensive nonconvex multiobjective optimization problems. The IHBE method has been developed so that a decision maker can conveniently investigate the objective space and learn about possibilities and limitations of solutions which are available for themultiobjective optimization problem at hand. In order to lessen the computational expense of the problem, an approximation of the Pareto front is used in the method. The approximation is based on a surrogate function and pre-calculated Pareto optimal objective vectors. By specifying desirable upper and lower bounds for the vectors, the decision maker makes queries about what kind of approximated Pareto optimal objective vectors are available. The method either presents approximated Pareto optimal objective vectors satisfying the bounds or helps the decision maker in setting the bounds in a way that approximated Pareto optimal objective vectors can be found.
Strategy and Manipulation in Medieval Elections
There are many goals in developing electoral protocols, including a desire for a system which is transparent, in that it is clear what the rule or procedure to follow is; nonmanipulable, in that it is not in a person’s best interest to misrepresent their preferences; honest, in the sense that it elects the ‘right’ candidate; and not open to strategizing, i.e., bribery or collusion. However, these desiderata are in tension with each other: Often, transparent electoral procedures are the least strategy resistant, and many honest procedures encourage manipulation. Thus a balance between these different goals must be sought. In modern times, since the seminal result on vote manipulation, the Gibbard-Satterthwaite Theorem [5, 6], much attention has been devoted to developing voting rules where manipulation is never in the best interest of the voters [4] or which are computationally too complex for the average bounded agent to be able to manipulate [1]. This focus on computational aspects of electoral methods is one of the hallmarks of modern studies on voting. But pursuit of these goals is not restricted to modern times: Those participating in elections in the Middle Ages also sought transparency, non-manipulability, honesty, and strategyproofness in so far as these properties can be consistently expressed in a single procedure. However, given the lack of computational sophistication in the Middle Ages, alternate approaches were needed in order to promote honesty, discourage strategizing, etc. These approaches can be classified as either external (constraints introduced outside of the electoral procedure, such as incentives for coming to consensus quickly) or internal (constraints introduced within the electoral procedure, such as voting rules which cannot be manipulated without adverse effects, or which are too difficult for the average bounded agent to manipulate). Surveying examples of both approaches in the context of medieval ecclesiastical and secular elections provides an interesting comparison to modern electoral procedures. Elections in the Middle Ages were used for the same reasons that they are today: To select suitable candidate(s) for a particular office, duty, or obligation. However, it is important to note that the term electio was used in the Middle Ages in a broader sense than our modern ‘election’. Its primary sense was ‘selection’ or ‘choice’, and only secondarily ‘election’ in the modern sense. Thus, many records which purportedly discuss elections are not discussing elections of the type which interests us. We can identify four categories of medieval electoral processes: (1) Election by an external authority having no direct interest in the election; (2) Indirect election, where electors name other electors who then select or elect the officials; (3) Election by lot; and (4) Election by ballot. Elections of the first and third types are generally computationally uninteresting; the first type corresponds to dictatorial voting rules, and the third type collapses to probability theory. In general, interesting voting methods are found only in the fourth type, election by ballot, though they can also occur in indirect election.