一般我們都將大眾假設為風險趨避者，由此，我們可以作出很多的推論，運用這簡單的假設前提，無論是風險學家，又或是經濟學家，發展出了各種不同的理論，這些理論成為現代風險、經濟之基石。

但當這樣的假設碰上了決策者風險偏好的問題，很多問題就出現了。由於風險趨避者的定義相當廣泛，它的條件是效用函數的一階微分大於零，二階微分小於零。建立於這樣的假設下，理論的型式很漂亮，但當我們要運用於現實中時，卻會發現種種的限制。

Central Dominance(CD)是一種當風險改變時需求變動的準則。這個準則建立於風險趨避者，如果所有的風險趨避者都會有一樣的需求變動的方向，那麼我們就可以運用這個準則找到答案。只不過風險趨避者含蓋甚廣，所有的風險趨避者如果對某種風險改變有一樣的特性，這個準則才能運作，反之，只要有百分之一，甚或是千分之一的風險趨避者碰巧有不同的需求變動方向，則這個準則就不能運作了。

因此，Huang,Tzeng and Shih (2012)以限定下的效用函數發展出了Almost Central Dominance(ACD)，其將經濟上不重要的人消除掉。這個理論的好處在於，它消除了部分該消除的人，因為通常有一些風險上的決策是顯而易見的，我們多數人都會選某A而不選某B，但是經濟上不重要的人通常會作出一些反直覺的事情，例如有些極端的風險趨避者認為十萬塊跟十億元對他們來說效用是一樣的，這就造成了在某些風險改變的情況下，這些人會選擇與大多數風險趨避者相反的決策。

這個理論探討了當風險改變，需求比例的改變。然而，決策者的效用變動也是一個風險決策上的一個重要的議題。Hollifield and Kraus (2009)曾為風險趨避者找出壞消息的準則。壞消息的意思是指，當風險改變，決策者的效用下降，投資在風險性資產上的比例也下降的情況。這個準則相當的簡單，他們發現了一個很漂亮的阿拉伯數字”1”，它界定了準則。本文想知道Hollifield and Kraus (2009)為風險趨避者定義的準則，是不是也適用於ACD，ACD是否也會有類似的如此簡單、漂亮的準則。

Generally, we assume public to be risk averse. Thus, we can make a lot of inferences, by using this simple assumption. Risk scientist or economist developed a variety of different theories. They became the cornerstone of modern risk and economy theories.

But the assumption of risk averse cannot be fitted with some problems of risk preference, due to the extensive definition of risk aversion. That is because its constraint is ”first-order differential utility function is greater than zero” and “the second derivative is less than zero”. Under this assumption, the type of the theory is very beautiful. But when we applied it in the reality, we found a lot of restriction.

Central Dominance (CD) is a theory for the criteria describing demand changes while the risk changes. The criteria are under risk aversion. If all the risk aversion investors have the same directions of change in demand, we can use this criterion to find the answer. But the definition of risk aversion is extensive. If all the risk aversion investors have the same characteristics, this criterion can work. On the other hand, the criterion cannot work as long as there is one percent or even a thousandth of the risk aversion investors have different direction of demand change.

Therefore, Huang, Tzeng and Shih (2012) developed Almost Central Dominance (ACD) by restricting the utility function. ACD doesn’t include the one who is unimportant economically.

This theory has the advantage that it eliminates some of the people who should be eliminated. There are some decisions of risk issue which are obvious. Most of us would choose A instead of choosing B. But economically unimportant person often makes some counter-intuitive decision. For example, some extreme risk aversion investors believe that one hundred thousand is equal to one billion is the same for them. It leads in some situations of risk change , these investor will choose opposite decision of most decision makers.

The theory explores the changing demand after the risk changes. However, the utility change of the decision makers is also an important issue of risk. Hollifield and Kraus (2009) used to define the bad news for risk aversion investors. The meaning of bad news is after the risk changes, the utility and demand of the investor both decline. The criterion of bad news is quite simple. They found a very pretty Arabic numerals "1".It can help us to be a criteria of bad news. This paper would like to know whether the criterion Hollifield and Kraus (2009) found is also applied to ACD or not.  

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2. Gollier , 1995. The Comparative Statics of Changes in Risk Revisited. Journal of Economic Theory 66 522-535

3. Huang,Tzeng and Shih , 2012. The Comparative Statics of Changes in Risk for Most Decision Makers. Working paper.

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