Friday, March 31, 2006

Interlude: Wen-zi's Art of War (Trojan pandas and character warfare)

Taiwanese government has officially rejected the CCP's offer of the pandas Tuantuan and Yuanyuan, under the pretense that island would be unable to provide proper care as required by animal protection laws and international agreements. This was, of course, a political response to the political can of worms acceptance would be opened (see March 29, 2006 post). As a supporter of the status-quo pending further democratic and human rights reforms in China, I am relieved by the decision. Unlike the Trojans, Taiwan has wisely turned down the CCP's pair of 'Trojan Pandas' - the ultimate diplomatic weapon.

Onto another topic: character warfare. I acknowledge that this news is a bit stale, however, it's probably something not many people noticed anyway. Last Thursday (3/23/06), the U.N. officially announced that it will cease to issue any material in traditional Chinese characters beginning 2008. Once again, the CCP has effectively hemmed in Taiwan's international prospects for recognition. Taiwan and Hong Kong are the only two places left in the world that continue to use traditional characters in their writing.


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Thursday, March 30, 2006

On devilish distributions and deviant divination Part 3

Finally I got some data! However, it's not the coffee data that I had promised. Still the story is the same. Only this time, it's looking at the toothpaste market. Exciting, isn't it?

Mkt % HH Freq
Shr Buying
Crest 29% 28% 2.1
Colgate 22 20 2.1
Aquafresh 12 14 1.9 Average 2.1
Mentadent 8 9 2.2

A & H 6 8 2.0
Ultrabrite 3 4 1.9
Listerine 3 6 1.5 Average 1.8
Pepsodent 3 3 1.8

Close Up 1.9 3 1.7
Aim 1.8 2 1.9
Sensodyne 1.5 3 2.0 Average 1.7
Oral B 0.6 1.4 1.3

Even before delving into model building, just looking at the data reveals surprising insights. First, I think I should explain the three columns. Column 1 is market share percentage. Column two is percentage of households of the sampling population that bought the brand at left. Notice that the percentages in this column unlike the first do not add up to 100%. This is because there is multiple product purchasing by households going on. The third column of numbers represent the frequency that they purchased over the period of 1 month.

Some insights:

First, the number 1 Crest has both larger market share and higher purchase frequency. Ehrenburg noticed this across all the markets that he's looked at. He has labeled this phenomenon 'Double Jeopardy'. Big brands win in two ways. They possess high market share and they are bought more frequently on average than the others.

Second, the notion of 'niche' markets is misguided. Most small toothpaste brands in this chart aim for a niche positioning strategy, but none of them achieved this in terms of having an especially high average purchase frequency. The closest was Sensodyne (for people who have sensitive teeth) at 2.0, but even that was lower than the average purchase frequency of the top 4 brands. The lesson is that in order for niche markets to exist in these mature markets, there has to be a particularly convincing reason, such as a captive consumer base, for it. In short, niches do not exist because marketers peddle their product that way.

Third, there is high variance with respect to market share and household penetration and very low variance with respect to purchase frequency. People's habits are difficult to change. Promotions and merchandising that aims to 'speed up' the rate of purchase for certain products are generally futile and rarely lead to lasting acquisition of new customers. This has major managerial implications. Market share and penetration are the key drivers of revenue and the best area to spend money. More on exploring this implication later.

The data in the raw form can provide a multitude of insights into consumer behavior. What if it were possible to actually model this behavior? Even though this data can be collected, doing so frequently costs resources and may be prohibitive. A model saves time and energy and at most needs only to be recalibrated occasionally with new data. Stay tuned, you'll wet your pants.

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Wednesday, March 29, 2006

Interlude: Wen-zi's Art of War: On Trojan Pandas

As I attempt to uncover a way to present my material of the Dirichlet model (how do I post pictures through blogger?), I'm going to take the time to write a post on something decidedly different: Panda Diplomacy.

Indeed, this is something that only the Chinese Communist Party can pull off due to their unique monopoly over the supply of pandas. Usually, the panda, seen as a national treasure by the Chinese, is given away to foreign countries selectively as a sign of goodwill and hope for continuing cooperative between the two nations (Why I say 'usually' will become clear in a moment).

The pandas, however, do not come cheaply. In the regulations governing the transfer of pandas to foreign nations, there is a line item that states that the foreign nation will be charged a sum of money for the right to keep the pandas. This fee in part pays for the expenses of the Chinese panda experts who oversee the entire process of transporting the pandas and training the zoologists who will eventually be taking care of their new charges. This fee is reoccurring so long as the panda resides in the foreign nation. The United States government pays a few million dollars just to keep the nine pandas it has in the country. Also note that these pandas are considered 'out on loan' by the CCP. They may be recalled at anytime, even before the entire length of their planned stay (~10 to 12 years) has run out.

So why am I suddenly bringing up all this about pandas? It has to do with Taiwan. Recently, the party chairs of two largest opposition parties in Taiwan, the KMT and the People First Party, paid 'goodwill' visits to China. They met a lot of important CCP members along the way and visited important financial and cultural centers, all the while giving speeches. As a sign of goodwill and sincerity for the detente in tensions between the two governments, China made an offer Taiwan could not refuse. Two pandas will be installed in Taiwanese zoos. This is where to politics begin.

The two pandas were named Tuantuan and Yuanyuan. The political innuendo could hardly be clearer. Tuanyuan in Mandarin means 'unification.' The plot thickens as Taiwanese politicians begin vigorous debate about the issue of accepting these pandas with those who oppose the deal led by incumbent president Chen Shuibian of the DDP. As if this did not stir up enough enough ruckus already, somebody had to point out that line regarding the 'fee to keep the panda.' That is, only foreign countries must pay this fee to keep pandas within their sovereign borders. Domestic transfers of pandas are exempt from this 'tax.' The CCP was openly treating Taiwan as part of its sovereign territory! What an ingenious subterfuge! Even I have to applaud the deftness of this action.

In short, no matter what happens, these two pandas cannot be taken in. If they are, Taiwan is implicitly acknowledging its status as a part of China. As a supporter of the status quo pending more democratic development on the China side, I would not like to see something like this happen at the moment. Anyway, I am not the one pulling the strings, so we shall see how Taiwan handles this pair of 'Trojan Pandas.'

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Tuesday, March 28, 2006

On devilish distributions and deviant divination Part 2

This feels like something only a MGMT concentrator would do. Please humor me, will you? After you are done with that one, follow up.

The Dirichlet model possesses the best explanatory power in mature markets. These are also known as near-steady-state-markets. While this property may seem to be extremely limiting at first, these types of markets are precisely the kind that can benefit the most from Dirichlet models. It's in the mature markets that brand managers are constantly trying to divine new ways to 'differentiate' their products from other offerings. The advertising battles waged in the mature markets are cutthroat and costly. What does Dirichlet have to offer?

The Dirichlet model offers patterns of consumer behavior that describe how they actually purchase. These are generalizable patterns which can be used to benchmark existing and new product performance.

Let's make the discussion more concrete and bring in a scenario. Suppose a U.S. coffee products firm is planning on introducing a new brand to the market. After calculating all the cash flows and developing the production process, it's time to market this thing. Call it CoffeeX. The marketing team gets cracking. They come up with two plans.

"Niche" - small number of people purchasing a large volume of product per period. Say 1% of the market buys the product 7 times during the year.

"Skim" - a large number of people purchasing a small volume per period. 7% of the market buys the product 1 time a year.

The members of the marketing department then proceed to get into a heated and passionate discussion about the relative merits of each plan. The Dirichlet model tells us they are just wasting their time (thinking of ways to waste ours). In mature markets, consumer behavior is largely predictable and, surprisingly, is a function of each brand's marketshare, penetration, and frequency. There are strict limits what marketing can do to change these behavioral patterns. Using the coffee industry, I'll upload a chart (which I don't have time to do today) to illustrate the relevant points.

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Monday, March 27, 2006

On devilish distributions and deviant divination

I admit to having a soft spot for anything that undermines orthodoxy. Paradigm shifts are beautiful. However my internal cynic chides me saying, "You just like it because you get a kick out of being sacrilegious and laughing at rank-and-file thinkers, you sadist!" I confess to being addicted to iconoclasm. That is why I find this amusing me to no end.

There is a small but fanatical group of people who worship at the temple of Dr. Andrew Ehrenberg, one of the great marketing thinkers of our times. I speak sarcastically because I am guilty of the same vice - except I claim to be a disciple of Peter S. Fader. Ehrenberg pioneered what his followers call the Dirichlet Model. It is the cornerstone of their entire religion - analogous to the resurrection of Christ in Christianity. Even though I make light of the model, I cannot deny its impressive track record. The core of the model has withstood the test of time. It is a highly applicable across all type of markets and industries and across nations.

Before I delve into the anatomy of the Dirichlet model (a wonderful exercise in itself), I should probably explain why I find it so amusing. Business managers today who work on the demand side - providing products or services - usually have a mental checklist they run through for ideas to grow their business. Looking at the jargon of marketing today, one can easily gain insight into what that list might look like: brand-building, differentiation, segmentation, and targeting. Managers focus on these things and hence set into action initiatives that try to achieve some (in-)tangible goal such as "increase brand-loyalty", "increase repeat-buying", etc. Business schools teach the same things because that's what the MBA's want to hear about, and let's not get started on the consulting firms. In short, this is the state of the establishment.

Now, enter the Dirichlet world, which tells us that all of this thinking is baloney/bologna. In the real world, these things that managers think about are not what dictates consumer behavior. The stultifying verdict is that their efforts are fruitless. The results of the Dirichlet Models and the actual data suggests that successful companies are not successful because of their unique positioning, branding, or promotional activities. What they can accomplish is actually far more limited. Marketing is not an "anything goes" science. The true dynamics of consumer buying behavior are built on something much simpler (well, sort of). The method to the madness might surprise you.

Simply music to my ears.

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Friday, March 24, 2006

Hill-climbing tedium Part 4

A differing opinion.

This is something I generally do not allow on this blog. It's for the same reason why I disabled commenting. In this domain, only my thoughts are absolute. I can even manipulate time itself as you can tell from all this backlog clearing I'm doing writing catch-up posts. However, it amuses me greatly to make an exception. Anyway, perhaps my view of human kind is too optimistic. There is in fact much reason to believe that we would sooner destroy ourselves inspite of our impressive qualities before achieving any sort of global maximum.

I do not retreat from my claim that humans are nature's finest creation. I still maintain that we have the ability to attain a global maximum (whose existence is debatable) even while we are at local maxima. We are not simple creatures bound to reacting to our environment. We can proactively mold and shape it. We can even go as far as create it. The crux of issue is that can we actually maintain the discipline required to reach a true maximum given that we have located it?

Human kind is plagued by myopia. Can we not help ourselves? In the astronomical time scale, a human is but a fruit fly. Our existence comes and goes in a blink. By our standards, ten years is a long time to see the results of actions come into fruition. Can we even comprehend what it means to make decisions that lasts from generations? Is it possible to internalize externalities that have not happened but will happen in the future due to events set into motion today? Humans do not have the patience to undertake massive inter-generational projects such as this. In a sense, does this make us hill-climbers focusing our attention from quarter to quarter, year to year?

We'd sooner destroy ourselves. How we squander our gifts! Is this what the Catholics call Original Sin?

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Thursday, March 23, 2006

Hill-climbing tedium Part 3

I have confided with a number of people that I believe that human beings are nature's solution to nature's own short-coming. That is, human beings have evolved an intellect that empowers them to achieve global maximums even when they have reached local maxima. They are not bound by the limitations of Nature Solver and so are not path-dependent. The hill-climbing algorithm is not the only way for humans to better adapt themselves.

I maintain that humans have the capacity - because of our intellect - to see global maximum solutions while we are at local maxima. Having seen the global maximum, we have the ability, should we choose to, to 'de-volve' ourselves, enduring a period of sub-optimal existence, in order to arrive at the base of the global maximum. This is a counter-intuitive mechanism that runs against the fundamental tenet of hill-climbing.

Humans can achieve their ends through indirect methods. This, combined with the knowledge of genetic/climatic/physical manipulation makes possible a new form of evolution. Humans need not be bound by the chance processes of natural optimization but can transcend it all by taking their future in their own (safe??) hands.

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Wednesday, March 22, 2006

Hill-climbing tedium Part 2

The achievement of the global maximum is path dependent. Depending on the initial position, a hill-climbing software/algorithm will take you to the highest local peak. That is all. There is no guarantee that the best solution has been achieved - only the one that happens to be the best in a local area. Could we think of biology in such a way? Adaptation and mutation take living organisms to a local maximum given a set of environmental variables. They are optimized for survival at this peak, but better solutions may be possible. In the event of a cataclysm, the environmental variables change, and what might have been a peak before has become a trough. Once again, nature's hill-climbing software takes each particular organism to their respective local maxima.

It's not a bad algorithm. The efficacy of the solution can been seen in the persistence of life despite the punctuated upheavals that marked the history of the Earth. Higher order organisms have evolved through the passage of time, being capable of far more complex and robust methods of survival than the mono-cellular organism that began it all.

Human being have always possessed a xeno-centric view of themselves. We are the ultimate predator on this planet and in some way, this makes us different from all other living things. We are not part of natural optimization because we can think our ways around the need physically adapt to hostile environments. That is why you can find human beings across all climate zones and on all seven continents. Yet, we forget that we were once lower-order life forms, subject to the natural optimization algorithm that binds all living things. Is there truth to our conceit or is it hubris that marks our imminent demise?

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Tuesday, March 21, 2006

Hill-climbing tedium

Recently working with some models in Excel (yes, baby software. I need to graduate to something for adults, like MatLab), I came across the inevitable frustration that plagues hill-climbing software like Solver. Once a model has more than 5 variables, you begin running the risk of multiple optima. With only 1 global maximum, how do you know you've reached the summit? Plugging in different starting values generally help. This exercise also led to Solver "blowing up" on me a few times. Luckily, I was left largely unscathed.

As the tedium of testing multiple scenarios began to set in, my mind wandered (as it usually does) to thinking about evolutionary hill-climbing. Isn't most of evolution just an exercise of incremental improvement when the environment in which the organisms live remain unchanged. Aside from the periodic cataclysmic events that precipitate sweeping changes in the surrounding, evolution is just adaptation through incremntal changes to better the likelihood of survival. It's Nature's hill-climbing software - Nature Solver.

But there are problems. Just like with Excel Solver, how does one know a global maximum is reached? Is is necessary that the global maximum is reached?

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Monday, March 20, 2006

Dirichlet and dervishes (Or how to keep students coming to lecture)

Being able to attend an institution such as Penn, I have had the pleasure of hearing the lectures of a distinguished array of faculty. Yet, even amongst a teaching population of this caliber, there are those whose classes I refrain from attending and there are those whose classes I attend with religious fevor. Those professors teaching classes in the latter category possess a sort of charisma that keeps students coming again and again.

A caveat: there are some classes you never want to go to, no matter the professor. OPIM 101 is a prime example. While there is perhaps no professor who cares more about undergraduates than Dr. Lee, the course material for OPIM straddles the fence between being too technical for the computer illiterate and too boring for the closet CS majors. The result is... Abomination (although very much improved by the time I took it).

What is the source of this charisma? Every good professor has to have a quirk - something that makes them memorable and endearing. From experience, the professors with undergraduate degrees from MIT are particularly good at this. Dr. Souleles has a compulsive check-marking habit. It takes about 5 to 6 (as much as 14 on one count) check marks where one would normally do. Dr. Fader has a whole arsenal of quirky things to dish out. There are special sound effects that go with graphing things on the board. He occasionally sticks his head into the hallway and yells random things during lecture. Once, he chalked up the walls of this $150M building to visually diagram a Dirichlet mixing distribution. I wonder who cleaned that up.

Quirks don't necessarily have to come in the form of odd behavior. They can also be jokes (albeit lame ones). A cell phone goes off in a finance class. "Is someone getting a margin call? You wouldn't want to miss that." There are also speaking quirks, but these tend to be annoying. Take for example speaking in Latin. Per se, ex post, ex ante, in vacuo, etcetera, etcetera. It's not so annoying if you knew what is means, but it takes time to get used to.

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Friday, March 17, 2006

Thinking about why we vote Part 8

Derivative, non-instrumental, non-separable processes. Voting is just such a process. In the majority of elections, the instumental value of a single vote is negligible in determining the final outcome, hence non-instrumental. Yet, voting has no value in-and-of itself since rigged elections have no purpose, hence non-separable. Therefore, act of voting must derive its value, but it does not do so through its efficacy of affect outcomes. Rather its value come from representation of a set or category of actions which possess or have a tendency to bring about positive utility outcomes - autonomy.

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Thursday, March 16, 2006

Thinking about why we vote Part 7

Deriving value through representation actions may explain why so many of the examples of preferences over comprehensive outcomes involve moral principles or rule-following. Principles and rules have the function of grouping actions together in categories. By adopting a principle, we make one action stand together with others and thereby change the utility or disutility of this particular action.

Principles are particularly well suited to creating representative relations. A single action comes to represent the entire class of actions. Thus even when the specific action is instrumentally negligible, the other actions it represents may have a much higher value. The symbolic relations created by principles, therefore, may make it rational to care about the "tendency" of a class actions, as opposed to the actual consequences of a single action. At a deeper level, being the type of person who acts on principles and conform to rules may itself be valued. If so, then actions that comply with a principle will represent not just the class of actions covered by the principle, but acting on principle itself.

Consider a pacifist who is deciding whether to participate in anti-war demonstration that is likely to raise the risk of a war breaking out. Being a pacifist, he presumably values the outcome of no war more highly than the outcome of a war. But given the choices between participating in the demonstration and increasing the likelihood of war and sitting at home, keeping the risk lower, it would seem that a principled pacifist may rationally prefer to participate because that action expresses or symbolizes his pacifist principle. His principles may commit him to fight war through vocal participation in anti-war efforts - a class of action that tends to make wars less likely even if this particular demonstration has the opposite effect. By instantiating this principle and representing the whole class of actions whose expected tendency is to promote peace, the act of demonstrating takes on sufficient value to outweigh the expected disvalue of making war more likely.

For a non-principled pacifist, on the other hand - one who simply prefers outcomes in which there less war, but is a pure instrumentalist when evaluating actions - such a preference over comprehensive outcomes would seem to be self-defeating, because the worse outcome resulting of his participation in the demonstration undermines any derivative value the choice act might at first have seemed to have.


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Wednesday, March 15, 2006

Thinking about why we vote Part 6

From the previous discussion, the imputing of value through symbolic relations has the potential to play a large role in the in the valuation of the voting process. There are two important points about symbolic valuation that is particularly relevant to the discussion of preferences over comprehensive outcomes.

First, the valued object/result that a process comes to represent does not need to be the same outcome that the process instrumentally achieves or tries to achieve. While the value of the process needs to be contingent on it having some causal connection to relevant result, the symbolic value does not need to be derive from that outcome.

Second, since a process can symbolize a different valuable result, there is no reason why the process should not derive more value or negative value from the objects it represents than from the result it causes. The participatory acts of voting have some (minute) instrumental effect on results. Yet the symbolically represent something much broader: our autonomy as agents who can shape our reality, rather than objects whose lives merely happen to them.

When what is symbolized is agency or autonomy, is it not surprising then that when voting should fail to symbolize or indicate autonomy they lose their causal connection with the events they are supposed to influence and hence lose their value?

Conclusion to follow.

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Tuesday, March 14, 2006

Thinking about why we vote Part 5

What endows a process with a non-instrumental value that is conditional on instrumental function? How can voting be non-instrumental and derivative when its value is conditioned on the ability of affect ultimate outcomes?

As stated before, derivation from instrumental value is simply not enough to explain the whole story. The standard model of value derivation is instrumental valuation: imputing the value from ends to means. Through their causal/instrumental relation to outcomes, the means derive their value. Thinking about it in another way, values travel back from outcomes to processes through the relation of process being a cause of the action.

Just like how value can travel back from outcomes to actions through a causal relation. The value of outcomes should also be able to travel back to actions that indicate or symbolize them through a symbolic relation. By indicating or symbolizing something valuable, by representing it, an action is endowed with symbolic value over and above its mere instrumental or intrinsic value. The idea may not be as far fetched as you think. The idea of advertising comes immediately to mind. Modern advertising, which associates the consumption of certain goods with certain desirable lifestyles or popular people, creates symbolically derived value by making the consumption of certain goods mark one as a certain type of person or symbolize certain virtues.

Voting may be non-instrumental and derivative, but it's hard to derive value from the end result because of the former attribute. It is also non-separable, which means it has no intrinsic value. This makes is a good potential candidate for symbolically derived valuation.

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Monday, March 13, 2006

Thinking about why we vote Part 4

Spring break was great. It was a chance to meditate and reorganize my thoughts.

Thus far: Voting is non-instrumental. It is non-separable. Yet, it is derivative. This is troubling.

There are two conundrums here. First, what does it mean to derive value non-instrumentally? Second, given a final result which is more desirable than another, having non-separable processes means that there is some process such that the lesser desired result may supersede the more desired one. For example, while former presidential candidate John Kerry may have received the popular mandate, U citizens on the whole would not have preferred that he be appointed to them without their say. Yet, when subject to the election machine of the U, Kerry lost. Save the snide comments when I say that there is such a process (non-separable, derivative) in which the more preferred outcome loses to the less preferred.

It's a paradox. The value of the process is conditional on its efficacy in producing intrinsically valuable results. Yet, it may cause an intrinsically less valued result to be ranked more highly when seen in conjunction with said process. It's self-defeating. If an agent makes decisions with respect to non-separable, derivative processes, they may frustrate the achievement of the most valued results on which the value of the process component was supposed to be dependent on.

How can we think about processes that make the intrinsically less valued result come out higher in comprehensive outcomes? Instrumentalist cannot be the whole story. A deeper understanding requires probing into the way the value of a process can be conditional on instrumental function, yet not equal to instrumental efficacy.

I am still going in circles, but the circle grows smaller.

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Friday, March 03, 2006

Thinking about why we vote Part 3 (On process utility)

Briefly on what has been discussed thus far: voting is a process which cannot be separated from end results, yet it is a process that has very little effect of what those end results might be. Where is the value in voting?

It's becoming clear that voting cannot be said to possess value in vacuo, that is, it does not have intrinsic value by itself. Therefore, let's define a comprehensive outcome as one that includes a reference to the processes through which the results come about. When considering voting in the comprehensive outcome context, it's important to note that the processes part (the way the results come about) are not valued intrinsically, but rather as paths to outcomes. There is a preference for participation in decision processes. In general, we often prefer results to come about through processes that give us a "voice." Yet the value of "voice" is not intrinsic. We put no value on "voice" if it is clear to us that it has no causal relationship with the outcomes whatsoever.

Given that the value the choice process is conditional on a certain causal efficacy, we are once again back to square one. Comprehensive value is derivative of end results, but we have already seen that this is not the case with voting. Confused yet? There's more to come. I'll get to the bottom of this, I promise.

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Thursday, March 02, 2006

Thinking about why we vote Part 2 (On process utility)

This feels like something only a MGMT concentrator would do. Please humor me, will you? After you are done with that one, follow up.

Well, the spending continues. January personal income and consumption figures came out yesterday. Income rose 0.7% in January month over month, up from 0.5% back in December. That's around 8.7% annualized growth! The rise is probably due to a strengthening labor market. The initial claims numbers today came out to 294K which is higher than the market expectation of 285K. Remember though that initial claims figures are extremely volatile from month to month. Unemployment is still trending down overall. Consumption rose even more than income: 0.9%. Guess what? Saving remains negative at -0.7%.

Thinking about voting once again. Process matters. But how much? And under what circumstances? Remember from the previous post, I noted that voting has a small, almost negligible instrumental value component. Maybe it's time to back-track and rethink.

Take for example an option between passing a test fairly with a possibility of 60% and a passing a test by cheating with a possibility of 60%. Since there is no difference in the outcome from either choice, preference of one over the other is strictly determined by the choice processes. Most people would choose to be honest (fair) when given these two choices (way honesty has evolved as a sustainable economic behavior may be a topic for a future post), because they place process value on the act of being honest. Cheating might even have negative value.

Can voting be characterized in the same way? That is to say are voters indifferent between getting Candidate A with a 60% chance with voting and getting Candidate A with a 60% chance via a dictate from a secretive conclave? The answer is obviously no. No one would vote (unless forcibly compelled) in an election when the outcome is already predetermined. In a rigged election, the utility of voting is close to zero and maybe even negative.

It would be a shame to stop here. Await Part 3.

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Wednesday, March 01, 2006

Thinking about why we vote Part 1 (On process utility)

Existing home sales dropped 2.8% in January month over month. Inventories of unsold homes rose to an 8 year high. It's slowing, the housing market is slowing

What is the value in voting? Or maybe let me rephrase the question: where does voting get its value? In a voting society, its members believe that the act of voting possesses deep meaning. The most common reason put forth is that the act of voting is a way to make one's voice heard. Or a mutation of this: voting is a way to make my opinion count.

But let's think about these two claims for a second. The turnout in any national or state (or maybe even local) election is such that the vote cast by any single individual does not matter in the outcome of the election. In other words, people may say that they attribute value to the act of voting because it is a process that affects an end which is (presumably) important to them. Voting has instrumental value. Yet empirically, a single vote cast is not going to swing the outcome of the election either way to any great degree. True, voting does have that instrumental component, but it is so small - to the point which it can probably be ignored.

Where is the value? I'm going to think more on this one. Stay tuned.

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