Suppose
a book or an expert on a chosen field has set of recommendations for the
government to solve a social or economic problem of the day. For example, Tony
Atkinson in his book Inequality:
What Can Be Done?
has given 15 recommendations to solve the problem of rising and severe inequality.
Or think like this. A government has instituted a commission to suggest some
policy measures to solve the issue of inequality. The committee comes out with
a bunch of recommendations. Now all these suggestions will be discussed and
debated vociferously. It will continue for months. A government concerned about
rising inequality wants to do something to reduce it. My puzzle is this:
1. Out of top 10 inequality
experts, six experts accept recommendations #1 through #10 and reject #11
through #15. And the other four experts reject #1 through #10 and accept #11
through #15. In effect we see all recommendations are rejected and accepted. What
should a government wanting to implement some of recommendations do? The
question before the government is: Which one it should accept (reject) and why?
2. In the process of
intense discussions top experts in the field will reject some recommendations
and will accept some. So, if there are 30 big stars in inequality research,
then 15 accepting strongly all recommendations and 15 rejecting strongly how to
accept those recommendations?
So,
how to accept recommendations when there is a sharp divide among experts ? On
what basis?
I
have one suggestion. Instead of asking the experts to say yes/no, we can ask each
expert to place their confidence or weights behind all suggestions. Then we
will aggregate all confidence or weights. The recommendation having highest
confidence will be the chosen over others for government action. Will it solve
the puzzle mentioned above? It may not because when an expert says yes (no), he
may give 100% weight or 90% weightage. But it will be very effective when
experts are uncertain about the efficacy of recommendations. If experts give
their views unbiasedly then this weighting scheme will work better.
Arrow's impossibility theorem largely states this problem of deriving a social welfare function. I am not aware of latest developments on this.
ReplyDeleteYour proposition might give solution. But I am not sure whether this can pass all the tests of ordering
here's Pankaj:
DeleteSantosh Bhai, it is bit patchy and not well placed (I am sorry for being critical about your writing, which I suppose as a peer I must do, hope you would not mind). You have divided experts into two uneven groups (Six Accepts & Four Rejects). If Six accepts (prob. of more than 0.5) that is 1 to 10 suggestions against Four rejects (10 to 15), then how it could be called all are ‘accepted and rejected’? Though, I understand your proposition, but, for general reader, clarity is needed!
Here goes Kiran (sent to my mail)
ReplyDeleteI have read your piece. Your argument seems convincing to me. Good use of statistics in decision making.
Oh! I had no idea that it would appear right here on your blog, else I would have argued more scientifically [kidding]!
ReplyDeleteTo Pankaj:
ReplyDeleteUmm, u seem not to have read carefully! He writes:
"..If Six accepts (prob. of more than 0.5) that is 1 to 10 suggestions against Four rejects (10 to 15), then how it could be called all are ‘accepted and rejected’? "
This statement is little problematic...first, i wl clarify his point "that how it could be called all are ‘accepted and rejected?" He complains that i hv divided experts into two undivided groups...but this unequal division has nothing to do with my point...All i said is this: some experts accept recommendations #1 through #10 and reject #11 through #15. And the rest of experts reject #1 through #10 and accept #11 through #15. Thus, we see 15 recommendations are accepted (rejected also)...all i am saying is all RECOMMENDATIONS are accepted.......i am not saying all EXPERTS have accepted (rejected) all recommendations....Hope, i clarified Pankaj's point....
Second, Pankaj seems to trust on higher probability....lets say 10 are big experts...the first four on the extreme "left" side and the rest four on the extreme "right". Lets say this divide is due to ideology...If this is so, how can u say just becoz 6 experts agree the first 10 recommendations, we wl implement them? Why do u give less weightage to other 4 big experts who are on the right side?
Here's a comment from Raghu Rajan (this comment is intended for Krugman):
"For economists who actively engage the public, it is hard to influence hearts and minds by qualifying one’s analysis and hedging one’s prescriptions. Better to assert one’s knowledge unequivocally, especially if past academic honors certify one’s claims of expertise. This is not an entirely bad approach if it results in sharper public debate.
"The dark side of such certitude, however, is the way it influences how these economists engage contrary opinions. How do you convince your passionate followers if other, equally credentialed, economists take the opposite view? All too often, the path to easy influence is to impugn the other side’s motives and methods, rather than recognizing and challenging an opposing argument’s points. Instead of fostering public dialogue and educating the public, the public is often left in the dark. And it discourages younger, less credentialed economists from entering the public discourse."
Read more at http://www.project-syndicate.org/commentary/the-declining-quality-of-public-economic-debate-by-raghuram-rajan#Xlo2wzGUe2FcbYDZ.99
Well, what I deciphered from your post is 'whom to believe and whom to not' when there is a diametric opinion among groups of advisors, and, consequently, how to make a decision more efficient. And, to address this puzzle, you have suggested weighing opinion, of course, subject to conditionality.
ReplyDeleteI appreciate your reply to my reply (which you have clarified, painstakingly) and substantiation from Rajan’s reply to Krugman’s, nonetheless, my curiosity remains. In your blog, I see these points to be contradictory:
• You have not presumed that two groups are identical in terms of weight. By which I mean Group-1 (Six Experts) and Group-2 (Four Expert) are alike, no matter, what their actual numbers are?
• If, they are not alike, and if we go for ‘weighing’ the ‘confidence’ in their decision then it will be skewed towards Group-1, since, decision is diametric (1 or 0).
• In both the cases, that is majority or weighing, Group-1 has an edge over its counterpart, hence, likely to be heard by the government.
Notwithstanding, while concluding entire episode, you seemed to be pessimistic about your own views: “But it will be very effective when experts are ‘uncertain’ about the ‘efficacy’ of recommendations.” I don’t understand what you do mean by ‘uncertain’ and ‘efficacy’? And, you also go on saying that: “If experts give their views unbiasedly then this weighting scheme will work better.” We know that all suggestion and recommendation comes along biasedness – ‘superiority of our theory over the other’ or ‘mine explains best than yours’. And, perhaps, this is the moot point of difference among the experts, then how they could be ‘uncertain’ about their recommendation. Perhaps, superficially!
Hope, your further clarification will lead me to clarity!
Disclaimer: I may not have grasped fully!
I wl start with your last para. No, I m not pessimistic. I am reather more realistic. I don’t claim I do have earth shattering solution. My view is rather nuanced, modest.
DeleteWhat do I mean by “uncertainty” and “efficacy”?
I wl give this example in macro context. Should the government unleash fiscal stimulus to offset the recession? A die-hard Keynesian like Krugman would say “yes” or weight of 1. A die-hard Keynesian hater like Robert Lucas, John Cochrane, Robert Barro would say “NO”, or weight of 0. But ask Greg Mankiw. He would say, umm, the theory says it will work, but empirically I m not sure. (Just to be clear: they all are having different opinions about the size of fiscal multipliers. Krugman may say, well, fiscal multiplier would be more than 1 or 1. But new-classical economists Robert Lucas, John Cochrane, Robert Barro would say fiscal multiplier is statistically not different from 0. Greg Mankiw believes fiscal multiplier would be around say 0.6, or 0.4.) In this example, Greg would is uncertain about the efficacy of fiscal policy or fiscal stimulus that the government plans to launch. So, he may put a weight of say, 0.6. I hope you see now what I am talking.
Regarding “unbiasedness”. Well, in that Greg is republican. Republicans don’t like big government. So, he tries to answer from an ideological point, he wod say the size of fiscal multiplier is 0 or a weight of 0. When I say, if experts give their views unbiasedly then this weighting scheme will work better, I mean to say they have to get rid of their ideological stance and try to answer this question as a pure academician or researcher.
So, if you do agree with the above, then I see you will find a solution to your question.
#1 So, if I divide the group numbers equally, you agree with me that the puzzle or the question which I have raised in my blog post makes sense? Yes, it is. But to me the number of experts in a group is irrelevant if they give opinion unbaisedly. (Do u see that? Read my example again) In fact, in real world, we don’t form a committee where we select 5 from left and 5 from right. In a real world, we have economist like Greg Mankiw! God is so great!
#2 your second is answered in that example. You see that?
#3 again clarified in that example.
Since when have the econ folks studying an inexact science begun rooting for clarity? :) :) A great deal of econ theories and empirics end up in laboured and grudging consensus, not an outright one like we see in basic sciences. Then, there is your behavioural factors that creep in, real-life recommenders try to balance between being politically correct and sounding (may not be forthright or real) good on theory. Political economics factors like government ideology, electoral cycles, and political competition etc. are the final deciders, they impact the ultimate level of acceptance/rejection of the recommendations.
ReplyDeleteSantoshbhai’s views seem and are good. However, if the blogger mathturbates a model to support his suggestion, it could be, well, clearer!