аЯрЁБс>ўџ 35ўџџџ2џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџьЅС5@ №Пš$bjbjЯ2Я2 "2­X­X€џџџџџџˆ˜˜˜˜˜˜˜Ќ8ШфЌH Ж"&&&&&&ЧЩЩЩЩЩЩ$ў RP ќэ˜&&э˜˜&&    .˜&˜&Ч Ч  ˜˜&ј №ЦЊ4wЦMjЧ 0H L З4L ЌЌ˜˜˜˜L ˜Ј&"H `tЋ&&&ээЌЌфы"ЌЌJonathan Katcher 5/13/06, 5/14/06 from ideas developed since 2003 Relevancy: Social Sciences, Economics, Prediction Markets Љ 2006 Jonathan Moses Katcher, All Rights Reserved THE ACTUATOR People do things. They have control over what they do. And generally they know what they are going to do before they do it. This is common sense, and an assumption of this paper concerning the event-actuating-agent, or actuator for short. The simplest example of an actuator is a coin flipper who uses the forced coin method of flipping, as opposed to the fair or biased coin method of flipping. The fair coin is fair (50/50), and the biased coin is biased in favor of one party (ie 30/70), who generally has superior knowledge of that bias. The fair and biased coins are very well researched. But forced coins have been relatively overlooked by science. Therefore though forced coins are not the principle topic of this paper but simply an illustrative example, I must nevertheless describe them in at least minimal detail. Let us consider two people: a person who calls heads or tails as the coin is tossed into the air (caller), and a person who flips the coin (flipper). The flipper uses a forced-coin method. There are only two possible outcomes: “heads” or “tails”. It is obvious that when the caller calls out “heads!”, the flipper will force the coin into the outcome “tails”. And when the caller calls out “tails!”, the flipper will produce the outcome “heads”. So no matter which choice the caller yells out as the coin is tossed into the air, the flipper will always produce the opposite outcome. This is because the flipper is rational and informed of his own abilities. Therefore he will always choose to behave in such a way so as to win the little zero-sum game occurring between him and the caller. Where cash is involved and each player is betting the other will be wrong, the flipper will be the one winning the money. What distinguishes this type of coin method from fair or biased coins is that the probability of heads is not set in stone so to speak. Instead, the probability is dependent on the decisions of the caller and the flipper. In the above example, the state-actuating-agent (actuator) was the flipper who could force the coin into either of the two possible states. But the idea of the actuator extends beyond the petty example of the forced coin. Let us consider two other examples: A profit-motivated terrorist, and a profit-motivated cancer researcher. In a binary prediction market centered around the event of an attack of a particular building, one can bet either in the affirmative (bet attack), or in the negative (bet no attack). Assume these two outcomes are the only possible outcomes. Our profit-motivated terrorist has no inherent preference for either outcome; his only motivation is profit. If he chooses to actuate the ‘attack’ outcome, it will certainly occur with 100% probability. And furthermore let us assume his costs are zero (he stole the required materials, and will never be identified or caught for any of his crimes). Let us also assume that he has no ability to decrease the probability of the ‘attack’ outcome. Unless the prediction market prices already predict 100% probability of attack, it will be rational (given this agent’s characteristics) for him to bet on, and then actuate the ‘attack’ outcome. When the outcome occurs, his contracts(the ‘attack’ contracts) will be worth $1 apiece, and the ‘no attack’ contracts will be worth $0 apiece. The idea of the actuator is equally applicable to more socially desirable behaviors, such as in the example of the profit-motivated cancer researcher. In a binary prediction market topic of a particular kind of cancer, there are two types of mutually exclusive and completely exhaustive outcomes: ‘cure’ or ‘no cure’. A person can bet either way. Assume that our cancer researcher has no inherent desire for either outcome. He does not care either way. If he does choose to actuate ‘cure’, then that outcome will occur with 100% certainty. Let us also assume that his costs for actuating ‘cure’ are zero. He has no ability to decrease the probability of ‘cure’. Unless prediction market prices already predict 100% probability of a cure, it will be rational (given this agent’s characteristics) for him to bet on, and then actuate the ‘cure’ outcome. When the outcome occurs, the ‘cure’ contracts will be worth $1.00 apiece, and the ‘no cure’ contracts will be worth $0 apiece. To simply state that the agent is an actuator is a meaningless statement. The correct way to state the role of the agent is: “The agent is an actuator with respect to such and such event”, or “the agent has actuator characteristics with respect to such and such event”. If not stated explicitly, the event over which the agent has sway must be stated tacitly by context. Furthermore, one cannot gauge from a statement “the agent is an actuator with respect to such and such event” what exactly those characteristics are. In the case of the forced coin example, simply stating that an agent has actuator characteristics with respect to the outcome of the coin flip is not sufficient information to tell you in what direction the agent can increase the probability. It does not tell you if that change is irreversible. It does not tell with what certainty the actuator’s action will produce the intended result. And it provides no information regarding the possible existence of other actuators in the environment who also have the ability to influence the probability of that same event. Furthermore it should be emphasized that the characteristics conferring upon an agent the ability to manipulate the probability of an event (actuator characteristics) are independent of that agent’s other characteristics and features. An agent’s actuator abilities state nothing about that agent’s desires, or preferences for the different possible outcomes of the event. An agent’s actuator characteristics do not even necessarily presume rationality. Though theories of rationality may involve a discussion of the actuator characteristic, the actuator characteristic is completely independent of the concept of rationality. Regarding information, an actuator can have inside information about what his actions will be in the future. In fact, he is generally the producer of this information. However, even an agent with no memory and hence no possibility of storing insider information can still be an actuator as long as he has the ability to influence the probability of the event. So the idea of the actuator can be completely separated from the idea of the selfish pursuit of gain. So while actuator and selfish characteristics often are related, they need not be. When considering real-life examples, these questions must be answered by searching for a mechanism. When constructing an ideal model, these questions must be answered by assumptions within the model about the mechanism. Despite simplifications in the examples above, the idea of the actuator is something that should be recognized, and that can and should be used for more complex analysis of these types of problems, problems that fall into the category of the event-based-betting paradigm; Problems such as those involved in prediction markets. PAGE  PAGE 1 !"B|Œ’ЎЏБНО€  › Ђ Ќ Ў А Ы в м ‚ ‰ ž Љ Џ Й з о ј љ њ P R Ж З є ї Л ц Š‹Œ—™žЅ+ghi<ДЕЖЛТmЇC%ќјєјє№ьшьј№фрмидадмЬиЬдЬдЬдЬдШЬдЬдФиФРФМФиФШФИШФШФДдАДЌЈАЌЈЌЄЌЈh<§h[єhc<hy(hг%Lh Ѓh„kуhWFйh—N hЬ=ћhѓќh !ќh…q hMЬhЉ5Ёh$Cьh1thŒбhZzЖht6h,3hYhзe?"B|ЏАБОПЎ Џ љ њ hiЕЖЕЖ‰Š8#9#€$њјјјјјј№јјјјјјыыыыыыыытй„а`„аgdWp„а`„аgd<§gdy($a$gd&v…gdзe€$™$ўў%ДЕЖшэ)LtпђЗаL‡ˆ‰Š˜§L^l„†ЛЩ”ПШ=hmІ З С у ё ў !Z!d!\"####7#8#9#@#P#f#о#$€$$‡$ˆ$‰$‹$Œ$’$“$ќјє№ь№ќ№ќ№ќьќьќшќшфшєрмриририрдаЬШЬаЬафифЬфЬфЬфдЬдЬдрдрФдФдшКДКДАКДКh+А h+А0Jjh+А0JUhМ8Dh Ѓh1thе=yhWphЫr5h„kуh%Kмhп Єhє#еh<§h[єhy(hг%Lhf@aD€$‰$Š$‹$–$—$˜$™$š$ѓъшѓъшшп„а`„аgdWp„h]„hgdЁ G „јџ„&`#$gdWFй“$”$•$–$˜$™$š$єъфрмиhє#еhŒбh+А h+А0Jjh+А0JUhŒб0JmHnHu 1hАа/ Ар=!А"А# $ %Аœ@@ёџ@ NormalCJ_HaJmH sH tH DA@ђџЁD Default Paragraph FontRiѓџГR  Table Normalі4ж l4жaі (kєџС(No List4 @ђ4 Ё GFooter  ЦрР!.)@Ђ. 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