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== do not sound a hundred heart back into his head ==
{{Tone|date=December 2010}}


Joseph was a smile, stunned to catch up to Lee Mei asked: '? How can you go.'<br><br>guarantee is I do sin hands, here I can simply reach of sin [http://www.dmwai.com/webalizer/kate-spade-15.html ケイトスペードニューヨーク 財布] ah, Caoya Jie hit a key, with one mind and said: 'Do not forget brother is clairvoyant company CEOs ......... their monitoring equipment is to go [http://www.dmwai.com/webalizer/kate-spade-5.html ケイトスペード 財布 セール] through [http://www.dmwai.com/webalizer/kate-spade-13.html ケイトスペード 人気バッグ] our public security and acceptance, and even many insiders that we sell to their equipment, you say such a [http://www.dmwai.com/webalizer/kate-spade-14.html ケイトスペード ハンドバッグ] device, how can the experts stumped me, want to know how the back door into it? '<br><br>He proudly said, Hey, do not sound a hundred heart back into his head, only to find all gathered behind him, and Yu Feng chuckled and asked: '? into the back door of how it feels.'<br><br>'yo, Caoge have this hobby.' mouse Road with, Li Mei, biting his lower lip angry, afraid to talk to each group of hooligans.<br><br>Caoya Jie cheap cheap smile, a touch of handsome hair, black jack knock an Enter key, a remote execution of the program, brush brush lit screen, a synchronized to [http://www.dmwai.com/webalizer/kate-spade-5.html ケイトスペード 財布 ゴールド] a monitoring unit here, mouse stunned with: 'Oh, This feeling is the back door into the great.
The '''Ellsberg paradox''' is a [[paradox]] in [[decision theory]] in which people's choices violate the postulates of [[subjective expected utility]].<ref name=Ellsberg1961>{{Cite journal |last=Ellsberg|first=Daniel|authorlink=Daniel Ellsberg|journal=[[Quarterly Journal of Economics]]|volume=75|title=Risk, Ambiguity, and the Savage Axioms|year=1961|pages=643–669 |doi=10.2307/1884324|issue=4 |jstor=1884324 }}</ref> It is generally taken to be evidence for [[ambiguity aversion]]. The paradox was popularized by [[Daniel Ellsberg]], although a version of it was noted considerably earlier by [[John Maynard Keynes]].<ref>{{Harv|Keynes|1921|pp=75–76, paragraph 315, footnote 2}}</ref>
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== 'hate it ...... people ignore you.' ==
The basic idea is that people overwhelmingly prefer taking on risk in situations where they know specific odds rather than an alternate risk scenario in which the odds are completely ambiguous-- even when mathematically the odds are identical.<ref>[http://agilelifestyle.net/ellsberg-paradox AgileLifestyle.net discussion on Ellsberg paradox]</ref>. That is, given a choice of risks to take (such as bets), people "prefer the devil they know" rather than assuming a risk where odds are difficult or impossible to calculate.<ref>[http://www.econport.org/econport/request?page=man_ru_experiments_ellsberg EconPort discussion of the paradox]</ref>


Focus, stretched out from the window head, looked one bedroom skirt, very proud of 姚曼兰 chest, 姚曼兰 a [http://www.dmwai.com/webalizer/kate-spade-14.html ケイトスペード時計人気] shame, [http://www.dmwai.com/webalizer/kate-spade-5.html ケイトスペード バッグ 激安] embarrassed, said:. 'I know you're the line'<br><br>'That night we try ...... or else?' I [http://www.dmwai.com/webalizer/kate-spade-9.html ケイトスペード 財布 値段] sin good direct, tongue licked his lips.<br><br>'Ah, and then talk to you, my face would not want to, it will not subtle point ah.' Yaoman Lan embarrassed authentic, sideways dodging.<br><br>'including ... including ...... mouth can, I do not mind.' I stretch Shenbozi [http://www.dmwai.com/webalizer/kate-spade-15.html ケイトスペード アウトレット バッグ] crime, bad smile.<br><br>have le to Yaoman Lan also hear this experienced man to the ears of the smell of urine, then deputy director Yin Yin I stared at his face, chances are an obscenity mouth, 'contain' forward is like? After stomping her embarrassed authentic: 'hate it ...... people [http://www.dmwai.com/webalizer/kate-spade-4.html kate spade バッグ] ignore you.'<br><br>said ran away, occasionally looking back Chou Chou, I can still see the face of the crime that immorality laugh.<br><br>what men have sex she does not accidental, but in fact done this degree so she surprises today to plug a small gift, bluntly pretend played.
Ellsberg actually proposed two separate thought experiments, the proposed choices which contradict subjective expected utility. The 2-color problem involves bets on two urns, both of which contain balls of two different colors. The 3-color problem, described below, involves bets on a single urn, which contains balls of three different colors.
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== he is a funny clown look ==
== The 1 urn paradox ==
{{unreferenced section|date=February 2013}}
{{OR section|date=February 2013}}


Wear more, I do not know sin hides, he is a funny clown look, or the cute guy roles, but months for the first time so close to the contact, the sense of excitement is always just lingering child ...... yes ah, so burning weather, he did not even An Jialu nose also clearly visible on the beads of sweat that crystal clear look, which [http://www.dmwai.com/webalizer/kate-spade-14.html kate spade マザーズバッグ] seems reflected his own shadow Ai<br><br>'Hey, God spoke all gone?' An Jialu found.<br><br>'ah, that there is, I attentively listening.' I sin stall road.<br><br>'Should not you say?' An Jialu smile, when a smile, greasy face on a small [http://www.dmwai.com/webalizer/kate-spade-3.html ケイトスペード リボン バッグ] shallow dimples, [http://www.dmwai.com/webalizer/kate-spade-13.html ケイトスペード 人気バッグ] good fresh to say. More than sin straining sip sip [http://www.dmwai.com/webalizer/kate-spade-11.html ケイトスペードニューヨーク 財布] straight swallow the saliva flow want to go, hard to ask: '? You let me say what.'<br><br>'such great pains to put forward a picnic, but also to engage in false [http://www.dmwai.com/webalizer/kate-spade-8.html 財布 ケイトスペード] Yifeng hand ...... not just to eat it?' An Jialu wise to look at the seemingly do not have a motive more than sin.<br><br>Damn, misunderstood, but just kind of misunderstanding, I sin smiled, straights
Suppose you have an [[urn problem|urn]] containing 30 red balls and 60 other balls that are either black or yellow. You don't know how many black or how many yellow balls there are, but that the total number of black balls plus the total number of yellow equals 60. The balls are well mixed so that each individual ball is as likely to be drawn as any other. You are now given a choice between two gambles:
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== with jubilation stomping ==
{| border=1 align=center
!Gamble A !! Gamble B
|-
|You receive $100 if you draw a red ball || You receive $100 if you draw a black ball
|}


Han jian your [http://www.dmwai.com/webalizer/kate-spade-1.html ケイトスペード 財布 店舗] style sao it?<br><br>knocking, knock, rattled seemingly disordered voices, Xiaomeng Qi did not understand that this is doing, Luo Jialong also holding chopsticks knock on, and Wang Shen repair [http://www.dmwai.com/webalizer/kate-spade-9.html バッグ ケイトスペード] unexpectedly laughed, [http://www.dmwai.com/webalizer/kate-spade-11.html ケイトスペード 財布 通販] joined the ranks of the bowl knock knock dish, knocking knock with, even Xiong Jianfei and mouse seems to have cheered up a ding ...... Dangdang, with jubilation stomping, then I say crime lead singing:<br><br>na [http://www.dmwai.com/webalizer/kate-spade-10.html kate spade ハンドバッグ] brother, my brother, the most pro is you.<br><br>mortgage, debt, the weight I do not play.<br><br>official, public grain, tired I straight pant.<br><br>flies are hard to force, who put who despise.<br><br>say all laugh, laugh Xiaomeng Qi direct spray, it seems that this is a summary of married life, and this one also opened a smooth like-minded people, who will [http://www.dmwai.com/webalizer/kate-spade-9.html バッグ ケイトスペード] take more than a question of sin, 骆家龙 is connected to the:<br><br>na brother, my brother, the most pro is you.<br><br>what conscientious, what dedication, it is for the play are special.<br>What<br>
Also you are given the choice between these two gambles (about a different draw from the same urn):
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== without long ==
{| border=1 align=center
!Gamble C !! Gamble D
|-
|You receive $100 if you draw a red or yellow ball ||You receive $100 if you draw a black or yellow ball
|}


A light? 'Yuan Liang Tao.<br><br>than sin took a deep breath, smiled, he knew, struggling in this state of mind is what [http://www.dmwai.com/webalizer/kate-spade-12.html ケイトスペード ハンドバッグ] kind of taste, he thought, seemed to try to figure out the person's credibility, he seems a long [http://www.dmwai.com/webalizer/kate-spade-7.html ケイトスペード バッグ 新作] while from the other side complex and clear eyes found the things [http://www.dmwai.com/webalizer/kate-spade-14.html kate spade マザーズバッグ] they need, opening with: '? Well, I ask you, if you have a chance to catch Wu Xiaolei, you will [http://www.dmwai.com/webalizer/kate-spade-2.html ケイトスペード トートバッグ] do it.'<br><br>'That, of course, we are not doing it?' Yuan Liang Tao.<br><br>'If this thing to break your bottom [http://www.dmwai.com/webalizer/kate-spade-14.html kate spade マザーズバッグ] line, you will do it? For example, I really put his parents in isolation, without long, according to the normal procedure to go on the trip.' I sin road.<br><br>Yuan Liang thought, nodded:. 'If necessary, you can do so ...... this unfinished case, the burden is on them, live every day in fear of the taste and feel good.'<br><br>'Well, we do this together, I am here to have a detailed plan, is looking for people to talk about ...... you are mentally prepared, you may want to touch your bottom line, you sure you want between us
This situation poses both ''[[Knightian uncertainty]]'' – how many of the non-red balls are yellow and how many are black, which is not quantified – and ''probability'' – whether the ball is red or non-red, which is ⅓ vs. .
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== go back to connect has slept mouse and Li Er Dong ==
=== Utility theory interpretation ===
Utility theory models the choice by assuming that in choosing between these gambles, people assume a ''probability'' that the non-red balls are yellow versus black, and then compute the ''expected utility'' of the two gambles.


, Identify and correct; then look for the Du flute that old thief, confirmation, in order to appease the old thief no longer go wandering become security risks, I sin also choreographed some yellow three dead nonsense. Almost on a busy morning, go back to connect has slept mouse and Li [http://www.dmwai.com/webalizer/kate-spade-3.html 財布 kate spade] Er Dong, ran non-stop trip airport to learn about the progress of the trial, went back to the city, [http://www.dmwai.com/webalizer/kate-spade-8.html 財布 ケイトスペード] came 娄雨辰 and Guo Feng's recent whereabouts, peripheral investigative task force to the Criminal Investigation Brigade and dual seven Public Security Bureau is responsible, and those back office, actually did [http://www.dmwai.com/webalizer/kate-spade-5.html ケイトスペード バッグ アウトレット] not work.<br><br>reminder is useless drops, now on this efficiency, more than the extreme crime has been tired, curled up in a police car after suv, whirring sleep, and 骆家龙 also support him, lying on the back seat complaining over sin snoring, soon He also snoring to [http://www.dmwai.com/webalizer/kate-spade-10.html ケイトスペード バッグ ショルダー] sleep on. Waking sleep two mouse and Lee Dong looked at each other, smiled and asked two mouse winter: '? Winter ah, you say what the two of them sleep dream is'<br><br>'I dream of a child Nvzei, Laoluo dream is to marry a white Formica come back.' Li [http://www.dmwai.com/webalizer/kate-spade-2.html ケイトスペード 財布 新作] two winter with a smile.<br><br>'I did not creative, everything really are
Since the prizes are exactly the same, it follows that you will ''prefer'' Gamble A to Gamble B [[if and only if]] you believe that drawing a red ball is more likely than drawing a black ball (according to expected utility theory). Also, there would be no clear preference between the choices if you thought that a red ball was as likely as a black ball. Similarly it follows that you will ''prefer'' Gamble C to Gamble D ''if, and only if'', you believe that drawing a red or yellow ball is more likely than drawing a black or yellow ball.  It might seem intuitive that, if drawing a red ball is more likely than drawing a black ball, then drawing a red or yellow ball is also more likely than drawing a black or yellow ball. So, supposing you ''prefer'' Gamble A to Gamble B, it follows that you will also ''prefer'' Gamble C to Gamble D. And, supposing instead that you ''prefer'' Gamble B to Gamble A, it follows that you will also ''prefer'' Gamble D to Gamble C.
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<ul>
When surveyed, however, most people ''strictly prefer'' Gamble A to Gamble B and Gamble D to Gamble C. Therefore, some assumptions of the expected utility theory are violated.
 
 
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===Mathematical demonstration===
    
 
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Mathematically, your estimated probabilities of each color ball can be represented as: ''R'', ''Y'', and ''B''.  If you ''strictly prefer'' Gamble A to Gamble B, by utility theory, it is presumed this preference is reflected by the expected utilities of the two gambles: specifically, it must be the case that
 
 
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: <math>R \cdot U(\$100) + (1-R)  \cdot U(\$0) > B\cdot U(\$100) + (1-B) \cdot U(\$0) </math>
 
 
</ul>
where <math>U(\cdot)</math> is your utility function. If <math>U(\$100) > U(\$0)</math> (you strictly prefer $100 to nothing), this simplifies to:
 
: <math>R [U(\$100) - U(\$0)] > B [U(\$100) - U(\$0)] </math>
 
: <math>\Longleftrightarrow R > B \; </math>
 
If you also strictly prefer Gamble D to Gamble C, the following inequality is similarly obtained:
 
: <math>B\cdot U(\$100) + Y\cdot U(\$100)  + R \cdot U(\$0) > R \cdot U(\$100) + Y\cdot U(\$100) + B \cdot U(\$0) </math>
 
This simplifies to:
 
: <math>B [U(\$100) - U(\$0)] > R [U(\$100) - U(\$0)] </math>
: <math>\Longleftrightarrow B > R \;</math>
 
This contradiction indicates that your preferences are inconsistent with expected-utility theory.
 
===Generality of the paradox===
 
Note that the result holds regardless of your [[utility function]]. Indeed, the amount of the payoff is likewise irrelevant. Whichever gamble you choose, the prize for winning it is the same, and the cost of losing it is the same (no cost), so ultimately, there are only two outcomes: you receive a specific amount of money, or you receive nothing. Therefore it is sufficient to assume that you prefer receiving some money to receiving nothing (and in fact, this assumption is not necessary &mdash; in the mathematical treatment above, it was assumed ''U''($100) > ''U''($0), but a contradiction can still be obtained for ''U''($100) < ''U''($0) and for ''U''($100) = ''U''($0)).
 
In addition, the result holds regardless of your [[risk aversion]]. All the gambles involve risk. By choosing Gamble D, you have a 1 in 3 chance of receiving nothing, and by choosing Gamble A, you have a 2 in 3 chance of receiving nothing. If Gamble A was less risky than Gamble B, it would follow that Gamble C was less risky than Gamble D (and vice versa), so, risk is not averted in this way.
 
However, because the exact chances of winning are known for Gambles A and D, and not known for Gambles B and C, this can be taken as evidence for some sort of [[ambiguity aversion]] which cannot be accounted for in expected utility theory. It has been demonstrated that this phenomenon occurs only when the choice set permits comparison of the ambiguous proposition with a less vague proposition (but not when ambiguous propositions are evaluated in isolation).<ref name=FoxTversky1995>
{{Cite journal | last1=Fox | first1= Craig R. |last2=Tversky |first2=Amos |authorlink2=Amos Tversky|year=1995|title=Ambiguity Aversion and Comparative Ignorance|journal=[[Quarterly Journal of Economics]]|volume=110|pages=585–603 | doi=10.2307/2946693|issue=3 | jstor=2946693 }}</ref>
 
===Possible explanations===
 
There have been various attempts to provide decision-theoretic explanations of Ellsberg's observation. Since the probabilistic information available to the decision-maker is incomplete, these attempts sometimes focus on quantifying the non-probabilistic ambiguity which the decision-maker faces – see [[Knightian uncertainty]]. That is, these alternative approaches sometimes suppose that the agent formulates a subjective (though not necessarily [[Bayesian probability|Bayesian]]) probability for possible outcomes.
 
One such attempt is based on [[info-gap decision theory]]. The agent is told precise probabilities of some outcomes, though the practical meaning of the probability numbers is not entirely clear. For instance, in the gambles discussed above, the probability of a red ball is 30/90, which is a precise number. Nonetheless, the agent may not distinguish, intuitively, between this and, say, 30/91. No probability information whatsoever is provided regarding other outcomes, so the agent has very unclear subjective impressions of these probabilities.
 
In light of the ambiguity in the probabilities of the outcomes, the agent is unable to evaluate a precise expected utility. Consequently, a choice based on ''maximizing'' the expected utility is also impossible. The info-gap approach supposes that the agent implicitly formulates info-gap models for the subjectively uncertain probabilities. The agent then tries to [[satisficing|satisfice]] the expected utility and to maximize the robustness against uncertainty in the imprecise probabilities. This  robust-satisficing approach can be developed explicitly to show that the choices of decision-makers should display precisely the preference reversal which Ellsberg observed.<ref>{{cite book |last=Ben-Haim |first=Yakov |year=2006 |title=Info-gap Decision Theory: Decisions Under Severe Uncertainty |edition=2nd |publisher=Academic Press |isbn=0-12-373552-1 |nopp=true |pages=section 11.1}}</ref>
 
Another possible explanation is that this type of game triggers a deceit aversion mechanism.  Many humans naturally assume in real-world situations that if they are not told the probability of a certain event, it is to deceive them.  People make the same decisions in the [[experiment]] that they would about related but not identical real-life problems where the experimenter would be likely to be a deceiver acting against the subject's interests. When faced with the choice between a red ball and a black ball, the probability of 30/90 is compared to the ''lower part'' of the 0/90-60/90 range (the probability of getting a black ball). The average person expects there to be fewer black balls than yellow balls because in most real-world situations, it would be to the advantage of the experimenter to put fewer black balls in the urn when offering such a gamble. On the other hand, when offered a choice between red and yellow balls and black and yellow balls, people assume that there must be fewer than 30 yellow balls as would be necessary to deceive them. When making the decision, it is quite possible that people simply forget to consider that the experimenter does not have a chance to modify the contents of the urn in between the draws. In real-life situations, even if the urn is not to be modified, people would be afraid of being deceived on that front as well.
 
A modification of utility theory to incorporate uncertainty as distinct from risk is [[Choquet expected utility]], which also proposes a solution to the paradox.
 
===Alternative explanations===
Other alternative explanations include the competence hypothesis <ref>{{cite journal |last=Chip |first=Health |title=Preference and Belief: Ambiguity and Competence in Choice under Uncertainty |journal=Journal of Risk and Uncertainty |volume=4 |year=1991 |pages=5–28}}</ref> and comparative ignorance hypothesis.<ref name="FoxTversky1995"/>
These theories attribute the source of the ambiguity aversion to the participant's pre-existing knowledge.
 
==See also==
*[[Allais paradox]]
*[[Ambiguity aversion]]
*[[Experimental economics]]
*[[Subjective expected utility]]
*[[Utility theory]]
 
== References ==
{{Reflist}}
{{Refbegin}}
* {{Cite book
  | last = Anand
  | first = Paul
    | title = Foundations of Rational Choice Under Risk
  | publisher = Oxford University Press
  | year = 1993
   | isbn = 0-19-823303-5}}
 
*{{Cite document | last = Keynes | first = John Maynard | authorlink = John Maynard  Keynes | year = 1921 | title = A Treatise on Probability | publisher = Macmillan | location = London | ref = harv }}
*{{Cite jstor|1911053}}
{{Refend}}
 
{{DEFAULTSORT:Ellsberg Paradox}}
[[Category:Economics paradoxes]]
[[Category:Economics of uncertainty]]
[[Category:Decision theory]]
[[Category:Decision theory paradoxes]]
[[Category:Utility]]
[[Category:Statistical paradoxes]]
[[Category:Paradoxes]]

Latest revision as of 06:07, 14 March 2013

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The Ellsberg paradox is a paradox in decision theory in which people's choices violate the postulates of subjective expected utility.[1] It is generally taken to be evidence for ambiguity aversion. The paradox was popularized by Daniel Ellsberg, although a version of it was noted considerably earlier by John Maynard Keynes.[2]

The basic idea is that people overwhelmingly prefer taking on risk in situations where they know specific odds rather than an alternate risk scenario in which the odds are completely ambiguous-- even when mathematically the odds are identical.[3]. That is, given a choice of risks to take (such as bets), people "prefer the devil they know" rather than assuming a risk where odds are difficult or impossible to calculate.[4]

Ellsberg actually proposed two separate thought experiments, the proposed choices which contradict subjective expected utility. The 2-color problem involves bets on two urns, both of which contain balls of two different colors. The 3-color problem, described below, involves bets on a single urn, which contains balls of three different colors.

The 1 urn paradox

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Suppose you have an urn containing 30 red balls and 60 other balls that are either black or yellow. You don't know how many black or how many yellow balls there are, but that the total number of black balls plus the total number of yellow equals 60. The balls are well mixed so that each individual ball is as likely to be drawn as any other. You are now given a choice between two gambles:

Gamble A Gamble B
You receive $100 if you draw a red ball You receive $100 if you draw a black ball

Also you are given the choice between these two gambles (about a different draw from the same urn):

Gamble C Gamble D
You receive $100 if you draw a red or yellow ball You receive $100 if you draw a black or yellow ball

This situation poses both Knightian uncertainty – how many of the non-red balls are yellow and how many are black, which is not quantified – and probability – whether the ball is red or non-red, which is ⅓ vs. ⅔.

Utility theory interpretation

Utility theory models the choice by assuming that in choosing between these gambles, people assume a probability that the non-red balls are yellow versus black, and then compute the expected utility of the two gambles.

Since the prizes are exactly the same, it follows that you will prefer Gamble A to Gamble B if and only if you believe that drawing a red ball is more likely than drawing a black ball (according to expected utility theory). Also, there would be no clear preference between the choices if you thought that a red ball was as likely as a black ball. Similarly it follows that you will prefer Gamble C to Gamble D if, and only if, you believe that drawing a red or yellow ball is more likely than drawing a black or yellow ball. It might seem intuitive that, if drawing a red ball is more likely than drawing a black ball, then drawing a red or yellow ball is also more likely than drawing a black or yellow ball. So, supposing you prefer Gamble A to Gamble B, it follows that you will also prefer Gamble C to Gamble D. And, supposing instead that you prefer Gamble B to Gamble A, it follows that you will also prefer Gamble D to Gamble C.

When surveyed, however, most people strictly prefer Gamble A to Gamble B and Gamble D to Gamble C. Therefore, some assumptions of the expected utility theory are violated.

Mathematical demonstration

Mathematically, your estimated probabilities of each color ball can be represented as: R, Y, and B. If you strictly prefer Gamble A to Gamble B, by utility theory, it is presumed this preference is reflected by the expected utilities of the two gambles: specifically, it must be the case that

RU($100)+(1R)U($0)>BU($100)+(1B)U($0)

where U() is your utility function. If U($100)>U($0) (you strictly prefer $100 to nothing), this simplifies to:

R[U($100)U($0)]>B[U($100)U($0)]
R>B

If you also strictly prefer Gamble D to Gamble C, the following inequality is similarly obtained:

BU($100)+YU($100)+RU($0)>RU($100)+YU($100)+BU($0)

This simplifies to:

B[U($100)U($0)]>R[U($100)U($0)]
B>R

This contradiction indicates that your preferences are inconsistent with expected-utility theory.

Generality of the paradox

Note that the result holds regardless of your utility function. Indeed, the amount of the payoff is likewise irrelevant. Whichever gamble you choose, the prize for winning it is the same, and the cost of losing it is the same (no cost), so ultimately, there are only two outcomes: you receive a specific amount of money, or you receive nothing. Therefore it is sufficient to assume that you prefer receiving some money to receiving nothing (and in fact, this assumption is not necessary — in the mathematical treatment above, it was assumed U($100) > U($0), but a contradiction can still be obtained for U($100) < U($0) and for U($100) = U($0)).

In addition, the result holds regardless of your risk aversion. All the gambles involve risk. By choosing Gamble D, you have a 1 in 3 chance of receiving nothing, and by choosing Gamble A, you have a 2 in 3 chance of receiving nothing. If Gamble A was less risky than Gamble B, it would follow that Gamble C was less risky than Gamble D (and vice versa), so, risk is not averted in this way.

However, because the exact chances of winning are known for Gambles A and D, and not known for Gambles B and C, this can be taken as evidence for some sort of ambiguity aversion which cannot be accounted for in expected utility theory. It has been demonstrated that this phenomenon occurs only when the choice set permits comparison of the ambiguous proposition with a less vague proposition (but not when ambiguous propositions are evaluated in isolation).[5]

Possible explanations

There have been various attempts to provide decision-theoretic explanations of Ellsberg's observation. Since the probabilistic information available to the decision-maker is incomplete, these attempts sometimes focus on quantifying the non-probabilistic ambiguity which the decision-maker faces – see Knightian uncertainty. That is, these alternative approaches sometimes suppose that the agent formulates a subjective (though not necessarily Bayesian) probability for possible outcomes.

One such attempt is based on info-gap decision theory. The agent is told precise probabilities of some outcomes, though the practical meaning of the probability numbers is not entirely clear. For instance, in the gambles discussed above, the probability of a red ball is 30/90, which is a precise number. Nonetheless, the agent may not distinguish, intuitively, between this and, say, 30/91. No probability information whatsoever is provided regarding other outcomes, so the agent has very unclear subjective impressions of these probabilities.

In light of the ambiguity in the probabilities of the outcomes, the agent is unable to evaluate a precise expected utility. Consequently, a choice based on maximizing the expected utility is also impossible. The info-gap approach supposes that the agent implicitly formulates info-gap models for the subjectively uncertain probabilities. The agent then tries to satisfice the expected utility and to maximize the robustness against uncertainty in the imprecise probabilities. This robust-satisficing approach can be developed explicitly to show that the choices of decision-makers should display precisely the preference reversal which Ellsberg observed.[6]

Another possible explanation is that this type of game triggers a deceit aversion mechanism. Many humans naturally assume in real-world situations that if they are not told the probability of a certain event, it is to deceive them. People make the same decisions in the experiment that they would about related but not identical real-life problems where the experimenter would be likely to be a deceiver acting against the subject's interests. When faced with the choice between a red ball and a black ball, the probability of 30/90 is compared to the lower part of the 0/90-60/90 range (the probability of getting a black ball). The average person expects there to be fewer black balls than yellow balls because in most real-world situations, it would be to the advantage of the experimenter to put fewer black balls in the urn when offering such a gamble. On the other hand, when offered a choice between red and yellow balls and black and yellow balls, people assume that there must be fewer than 30 yellow balls as would be necessary to deceive them. When making the decision, it is quite possible that people simply forget to consider that the experimenter does not have a chance to modify the contents of the urn in between the draws. In real-life situations, even if the urn is not to be modified, people would be afraid of being deceived on that front as well.

A modification of utility theory to incorporate uncertainty as distinct from risk is Choquet expected utility, which also proposes a solution to the paradox.

Alternative explanations

Other alternative explanations include the competence hypothesis [7] and comparative ignorance hypothesis.[5] These theories attribute the source of the ambiguity aversion to the participant's pre-existing knowledge.

See also

References

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  • 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534

Template:Refend

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    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

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  2. Template:Harv
  3. AgileLifestyle.net discussion on Ellsberg paradox
  4. EconPort discussion of the paradox
  5. 5.0 5.1 One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

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  6. 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

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  7. One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang