Showing posts with label game theory. Show all posts
Showing posts with label game theory. Show all posts

Monday, May 30, 2022

Stock Picking: The Game Within The Game

It is important to understand the game you’re actually playing in all endeavors. In stock picking among other areas of active investment many times the game that is being played is not the one that is at first perceived. It is also not always the one commonly believed or advertised to be being played. 

Goldman Sachs is on the other side of grandma's trade. Grandma and her investment club might have been putting in some pretty good research, but they’re very unlikely to outperform the models and information advantage a firm like Goldman Sachs will have. 

As general investors selecting exposure to the market when we evaluate Goldman Sachs, we evaluate them against the market. That is the correct benchmark for a potential or current investor as that is the central question: Am I better off investing with this particular active stock picker or is there another that can do a better job including using a passive index fund? Perhaps more appropriately and completely the question really is: Is the performance Goldman Sachs delivered appropriate for the risk taken, and could I have achieved as good or better results with as much or even less risk? 

That is the game we are playing when we choose investment in a fund manager, but that is not the game that Goldman Sachs, a fund manager, is playing. Goldman Sachs is not trying to beat the market per se. Goldman Sachs and more precisely specific fund managers within the large organization that is Goldman Sachs are trying to beat grandma and her investment club along with all the other relatively novice investors in the market. 

Personally as a wealth manager I am trying to help clients reach financial goals by investing so that their risk-adjusted return is appropriate for them. That is the game I am trying to play--rather than trying to beat the market, I am trying to match their risk/return exposure to their goals. That might mean using a Goldman Sachs fund if I think it is the best option in that specific area. 

Yet clients often don't want to play that game. In wealth management one of the more frustrating things to deal with is competing against mythical portfolios that clients think exist. An example of which might be when a client is told stories at the country club or down at the barbershop about how great someone else’s portfolio is performing. 

It is very difficult to compete against a phantom. Floyd in the barbershop is probably not doing as well as he claims. In fact it is very likely Floyd is under performing the competition because the competition for Floyd is Goldman Sachs among others. 

For Floyd to feel good with his investments, he only has to compare himself to those decisions he happens to remember along with hypothetical investments he did or did not choose to make. Floyd’s benchmark is cash and imagination. 

For Goldman Sachs to succeed they specifically have to beat most of the Floyds out there and only loosely do they need to keep up with the market. In the long run they probably don’t stand a chance against the market but in the long run that’s not who they really are competing against. 

For those of us who want to be investors with Goldman Sachs, the proper benchmark to compare them to is the market. But the bottom line for Goldman Sachs is a benchmark against Floyd, and Floyd never stood a chance. 





Friday, February 25, 2022

What All The Pundits Are Getting Wrong About CFB Playoff Expansion

In the subculture that is major college football, big news broke earlier this month that the championship playoff at the sport's highest level, FBS, would not be expanding from the current 4-team format for the duration of the current contract.

from CBS Sports:

Many of us who follow the sport found this disappointing. In fact almost everyone weighing in on it including the people who decided the matter by voting against expansion expressed disappointment. So what's going on here?

Most pundits write it off as simply a group of people too petty and short-sighted to get past themselves and grasp the bigger picture. To be sure, that might actually be true. However, I think there may be something else at play. 

College football is in incredible flux. From the rise/revolt of the student athlete finally demanding and getting a fairer seat at the table to competitive pressures to realign into better and better deals, there is much uncertain about its future. 

I think it is fairly obvious that the current arrangement in college football is not sustainable. There are currently 130 teams in the division with four more planning to make the upgrade from the lower-division FCS. This is a league that ranges from Alabama to Kansas (winningest to losingest over the past 10 seasons). That is a big range.* The bottom of the league would typically be an extreme underdog to any opponent from the top of the league--perhaps on average a matchup between a top 20 team and a bottom 20 team would imply a +90% likelihood the favorite would prevail.

This is not a league with any sense of balance. Frankly, somebody has gotta go. Most of the members of the major conferences, the so-called Power Five, know this. As a group their teams are much better than the rest of the league, the so-called Group of Five. While some of the weakest teams are found in the Power Five (e.g., Kansas and Vanderbilt) and some of the strongest teams are found outside the Power Five (e.g., Central Florida, Boise State, and independent Notre Dame), these are exceptions. 

It is my contention that the major stumbling block to expansion of the CFP before 2026 is what kind of deal the Group of Five would get in the arrangement. If those conferences were granted slots in the playoff, they would hold a lot of bargaining power going forward. The teams within those conferences, especially the very good teams, would have much less incentive to move into a power conference. If nothing else, the buyout of those rights would grow astronomically. 

It has been at least rumored that the Power Five have offered to buy out the Group of Five from the CFP. This would line up with my hypothesis nicely. The elite teams and conferences see the writing on the wall. They know, I believe, that the highest division of college football should have perhaps 64 or so teams in it. 

They also know, I believe, that even if a field of ~130 teams continues, it very well might be one with a de facto two divisions (upper and lower). The lower teams would be there as sort of a relegation à la soccer. By no means in this arrangement should a lower-division team have anything but the slimmest of chances at a playoff berth. 

Any concession made today to a lower-tier team/conference, is very risky. As talent accumulates into the better teams/conferences, those entities have the luxury of wanting a bigger share of the spoils. Negotiations while the future of the league is still sorting itself out means deals can't come together--the lower-level teams/conferences want more than they can offer and the upper-level teams/conferences need more than they can get. 

I didn't see this clearly at first and expected an expansion to happen before the current contract's expiration in 2025. Now I understand it better if for no other reason than having to look hard to understand why a deal fell through. 







*If you don't agree that Kansas isn't a serious team (Texas Longhorns probably don't), then consider the other doormats over the past decade: UMass, New Mexico State, Connecticut. 

Monday, January 17, 2022

Losers Don't Pay Taxes

This is just a rambling thought experiment. Feel free to ignore as it probably has vast shortcomings I have not considered in the admittedly short amount of time I have spent on it.

What if we instituted a rule via Constitutional amendment that the voters for a losing Presidential candidate in the general election do not have to pay federal income taxes for the term of office for which their loser was running? Suppose further that this amendment was so firmly established that there would be no question of it being followed (unlike so much of the Constitution) and no question of it being permanent for the foreseeable future.

I can think of lots and lots of problems with this as I'm sure you can too. A chief one is that Congress and not the executive branch determines taxes. Not to sideline those, but let's jump straight into some game theory.

What might some implications be?
  • Any rational potential voter would probably chose to vote given the prospect of tax avoidance.
  • Those votes would likely gravitate at first to candidates who looked very unlikely to win.
  • This seems to help third parties get on to ballots and garner significant vote share.
  • Knowing that everyone else is pursuing this strategy, voters likely would be reluctant to throw their vote for scary candidates. Even if they realize their vote will not affect the outcome of the election (spoiler alert: your vote doesn't matter mathematically), if presented with two similar candidates where one was slightly less objectionable than the other but both rather unlikely to win, the better of the two would tend to get the vote.
  • Candidates would know all this as well. That should push them to be slightly more objectionable at the margin. However, power still matters and is desired. So they would also have an incentive to try to win if they thought they could win. Now what would make them very desirable to getting votes so as to win? hmmm? Promises for very low taxes of course.
  • Could they or would they promise no taxes? I think this is unlikely as everyone knows that there have to be some taxes if there is to be some government spending. What about funding spending exclusively through debt, which is promises of either future taxes or future inflation? While this could be a workaround, it would have problems. The threat of inflation harms current voters as once inflation is suspected and to the degree it is suspected, it arrives immediately, or at least eventually. Future taxes might come soon enough to affect current voters and will likely affect their offspring, a group for which voters care.
  • This is starting to sound like a powerful tool to restrain government. Candidates are encouraged to campaign on small government so as to allow for low taxes. Voters are encouraged to support candidates who pursue small government. It also seems to promote experimentation as candidates are encouraged to be a bit wacky but not too wacky for fear (by voters) that they would actually get elected, and voters are incentivized to vote for marginally more wacky candidates (more than current but less than the wackiest). Here wacky means stuff like: drug legalization, troop withdrawal/de-escalation, privatization, deregulation, etc. Consider me wacky, btw.
  • I would fear it would degenerate into some suboptimal game, though, like where we all pretend to pursue small government and then don't actually do it leading to a need for higher future taxes. This would create a ratchet effect making the next election a competition between greater liars offering lesser improvements. Another BIG problem relates to the issue raised and promptly ignored at the top: Congress. Would Congress be emboldened to spend more? An opposing-party Congress as compared to the President seems likely to. This could not be fixed by changing the amendment to instead be a voter for a losing party in the next Congress since we don't vote for one Congressional position. Would the rule need to be it applies only to straight-party voters? If we went down that road, perhaps we would need another amendment limiting all elections to just two parties--the default situation we have now anyway. Lock in the Democrats and Republicans granting them the oligopoly of two. This might work making them compete along the tax dimension axis almost exclusively with all other policy subservient to it. Now we might be back to strong incentives for small government. Yet another suboptimal result might be one party in each election is always aiming to be the losing party and the other party tacitly agrees to be the winning party. Would this still give a small-government outcome? Maybe. Voters can switch who they vote for, but if there is strong lock-in on policy, they may not be so quick to change their votes. Where does social desirability bias and virtue signaling come it?
  • Who knows? I do like the integrity of only the voters who supported people in power have to pay for the actions of those people. 


Sunday, May 9, 2021

Does Ranked-Choice Voting Really Work?

All else equal, it would be good to reduce divisive partisanship in politics and to get elected officials who are more generally representative of their constituents' views. At least it seems like that would be good. Upon typing it I immediately have my doubts that I can both defend those goals as meaningful and desirable. And even if I can, it might be ridiculous on its face with the "all else equal" qualifier being impossible.

After all, all else equal, I would love to be worth $100 billion.

Regardless, let's briefly explore one possible method of improving elections, ranked-choice voting (RCV); aka, instant-runoff voting. From Ballotpedia ranked-choice voting is
an electoral system in which voters rank candidates by preference on their ballots. If a candidate wins a majority of first-preference votes, he or she is declared the winner. If no candidate wins a majority of first-preference votes, the candidate with the fewest first-preference votes is eliminated. First-preference votes cast for the failed candidate are eliminated, lifting the second-preference choices indicated on those ballots. A new tally is conducted to determine whether any candidate has won a majority of the adjusted votes. The process is repeated until a candidate wins an outright majority.
Let me state up front that I very much like this as something that might help break the two-party duopoly that corruptly prevails in America today. This is a goal that isn't necessarily in line with the reasoning that RCV could reduce divisiveness, etc., but I think it is consistent with those goals. 

Yet a simple but extreme thought experiment gives me some doubts about RCV as a cure for the supposed ails. 

Consider this election ballot: 
  • Jesus
  • Almost The Devil
  • A Goofball
  • The Devil
Now suppose that we hold the election and the first-place results are:
  • Jesus - 38%
  • Almost The Devil - 30%
  • A Goofball - 20%
  • The Devil - 12%

Under RCV we don't yet have a winner because no candidate has a majority. So, we eliminate the lowest first-place vote getter and give his second-place votes to the remaining candidates. Presumably in this hypothetical everyone who voted for The Devil, who has now been eliminated, put Almost The Devil as second place. Therefore, the new results are:

  • Almost The Devil - 42%
  • Jesus - 38%
  • A Goofball - 20%
We still don't have a majority vote getter; so we now eliminate A Goofball whose voters equally split their votes for Jesus and Almost the Devil as second place. Therefore, the new results are:
  • Almost The Devil - 52%
  • Jesus - 48%
My hypothetical has resulted in Almost The Devil defeating Jesus. That seems bad on its face. Additionally it probably does not satisfy the Condorcet criterion (a known short coming of RCV among other systems). This is just one way RCV might not live up to our dreams. The Volokh Conspiracy at Reason explores another, similar dampening of expectations for what RCV can achieve in heavily contested elections. 

My hypothetical concern here might be rejected for at least one of two reasons (or both): 
  1. In repeated experience voters should get better and better at using the new system. This is similar to rejecting the argument that a simple one-time experiment in a classroom "proving" prisoner dilemma problems mean people will fail at coordination ... therefore, government force is required to make them make the right choices. 
  2. Don't let the perfect be the enemy of the good. If this is a 90% solution to known problems with elections and democracy, it might be worth this hypothetical, unlikely risk.
Perhaps mine is an uncharitable view on the electorate in general. The thing is when I apply the labels (Jesus, The Devil, etc.) so as to be self evident about the hypothetical candidates you get an unfair look into the future that is not visible to the voters ex ante. Reasonable minds will be rationally ignorant about specific candidates, and no amount of homework done ahead of time will tell us the future with certainty. 

Perhaps it is an argument against democracy--one could charitably say it is simply an argument in favor of less democracy. I think it is certainly an argument for less government power. Electing Almost The Devil as Advisement-Only Czar to the Local Private Firm Dog Catchers minimizes his tyrannical reach. 

I still think RCV is a big step in the direction of improvement. But this thought experiment has given me some moderation in my expectations of what it can achieve. 


P.S. See also this podcast from Building Tomorrow for an overview on RCV and its potential implications. 



Tuesday, June 23, 2020

The Future of Education Post COVID-19

Tyler Cowen pointed to this “debate”, which I was a bit disappointed in for being too much an untethered discussion. Tyler’s portion I found more meaningful, but still it didn’t do much to advance my thinking.

Since they didn’t really have an objective topic, I guess I shouldn’t be too critical. But I find that a lot of the recent thinking on how things will change in the age of COVID-19 to be like this—not very deep, a combination of wish list and fear. My own view is an attempt at nuance between "most things will change very little" (we will snap back to prior norms) and "this epoch event has accelerated by multiple years that which was already underway" (e.g., teleworking just leapt forward at least 5 years along the prior trendline). To be clear I think holding both views is the best prediction--that is the nuance. Not a lot will change, but that which was already changing has been accelerated. 

Here are some of my thoughts regarding changes in education (both what was already happening and how they have accelerated) as well as the obstacles faced (incumbents and traditionalists don’t go down without a fight).

Elementary and High School

  • The major role of babysitting that school plays for many families has been shown to be replaceable. Schools aren’t as essential as previously imagined.
  • While the pandemic-induced schooling-from-home experience was miserable for most of us forced into it, schooling from home was already widely assumed to be awful. Now many are probably seeing arrangements other than traditional school as decent substitutes.
  • Much of what kids do in elementary school has little to no benefit for them. This is likely much more widely realized or at least considered as parents got a more up-close look at their kids “learning”.
  • For the kids trapped in poor schools, online and other arrangements now look like realistic improvements.
  • Teachers and schools that cannot provide good online options and flexibility have been considerably exposed.
  • For students old enough to not need babysitting and for those capable of learning outside of the regimented classroom (perhaps a large majority of students are in this latter category), questioning the necessity of a 7 to 8-hour daily routine is rising.
  • Unions and bureaucracies will be as formidable obstacles to change. However, they have a conundrum: teachers, administrators, and parents are afraid of the risk of infection. All of this pushes for alternative options to be explored, which drive experimentation toward alternatives that threaten the existing power structure.
  • Status quo bias/inertia are also obstacles. People tend to be very traditional when it comes to choices for their children. It is hard for them to wrap their heads around questioning the conventional wisdom narrative of school as we know it--especially government school.
Higher Education

For higher education I think we should solve for the equilibrium and use a typical university, the University of Oklahoma, as an example.

  • Although non-profits are insulated from market forces, they are still subject to the strength of the underlying economy on which they draw resources as well as the philosophical support of those in power. For universities those in power includes donors, alumni, legislators, employers of graduates, purchasers of research, and the public zeitgeist. So where are these headed? Saying that expectations will be to do more with less is a considerable understatement. Donor money and state funding will be much lower for a long time. However, desires/demands of universities will continue with smaller changes in overall goals. We will continue to virtue-signal about college-education being great hope for the future. So….
  • How does OU do more with less? By outsourcing what is not in their core competency. Why would we have students show up in a gigantic auditorium to watch a professor repeat a lecture he has given every semester for a decade plus? What is the value in having everyone in that room squinting at the board from the back rows and trying to avoid the inherent, multiple distractions? Can’t that be done online without the risk of infection? And once you realize that it can, it is just one more step to realize not each and every university need duplicate the tasks. Rather have grad students available to perform office hours and optional workshops. What is the point in offering the ~100th best programs in this, that, and the other? Partner with other universities for those services especially the undergrad basics. Specialize in only that where there is comparative advantage. For OU that might be areas like petroleum engineering, social networking, and football.
  • Social networking? Yes, with one of the biggest/best Greek life systems in all of higher ed, OU is among those that offer this feature. Even if the benefit is only perceived rather than real, perception matters to consumers. Drinking Gatorade doesn’t make you a better athlete.
  • And football? Yes, the football team is a source of revenue and marketing for the university. OU is great at it. And OU is in a much better position than most now that paying football players for their value contribution is rightfully (finally) trending to be the reality.
  • Thinking more of the general case, these trends lead to barbell effects: niche schools (elite quality where average is very much over) and enormous diploma-producing machines (economies of scale). While this is probably a trend within the realms of both undergraduate and advanced degree programs, it is more so a trend between these levels because . . .
  • The line between high school and undergraduate college will blur greatly while the line between undergraduate and graduate work will likely sharpen. This latter division will resemble the distinction that once existed between high school and major university such that grad school becomes the new, true higher education. 
  • Universities need to maintain their status (true in either the human capital model or the signaling model). To do so will require some exclusivity, which I think comes mostly at the entrance process to grad school--getting accepted to graduate programs becomes much more difficult. 
  • What happens to research? More rent-a-lab, rent-a-brain with corporate interests outsourcing to universities more than ever and universities renting away these resources. 
  • Obstacles? The same forces as above are at work against change here, and they are probably more powerful. But the stakes are higher and the willingness to experiment is probably higher too.
  • The major universities aren't going away, but they may be transforming so much that what emerges over the next ten years is vastly different from what we've known for so long. Imagine "going to" a major university, but not directly taking but a few classes there until upper-division-level work.
P.S., John Cochrane had two great posts recently on this topic (here and here).

Thursday, February 27, 2014

Everybody Talks

Listening to a recent Freakonomics Radio episode about gossip got me thinking about journalism and the perhaps unintended role it plays or has played in regulating society some. In the episode we first hear about research by Thomas Corley summarized in his book "Rich Habits" that showed the behavior differences between rich people and poor people. One of the differences he found was that the rich gossip significantly less than the poor. However, the rest of the episode tends to dispute that finding.

What stood out to me was how necessary the role of gossip seems to be for many aspects of society (e.g., norm setting and regulation) and how differently we approach and are affected by gossip. It doesn't seem at all unlikely to me that the wealthy would have different gossip habits and methods than the poor. The rich have different tools--namely, they have journalism. Or at least they had it until those crazy kids started TweetBooking everything.

Here is a theory that probably isn't original to me. I am not completely sold on it myself; it's just a hunch that I think at least partially explains what we've seen.

The rich and powerful have traditionally exerted a lot of control and influence over news media. This part is not in dispute. The creation and growth of news media served two primary purposes: 1) it had an informative value (stock reports, political actions, etc.) and 2) it had an entertainment value (local celebrity news, sports, etc.). But the problem is aside from the cut and dried factual reporting like the price of wheat or the winner of the mayor's race, most news reports have some damaging aspect to them that someone would like to keep quiet. These could range political corruption to a juicy, high-profile divorce to, well, the price of wheat for the guy who is trying to buy at a market discount. When we get down to it, the fact that we have journalism and that the rich and powerful put up with it seems a bit of a puzzle.

So what explains journalism as we know it--journalism that reports the good, the bad, and the ugly for the most part about both the rich and the poor? I think game theory offers a solution. The idea is that journalism is a necessary evil. Basically the job description was artificially created because the role was needed more than it was wanted. This puts it at odds with the idea that journalists are noble superheroes with special investigative and truth-finding powers striving to do good--journalists aren't that special, just don't tell them that. Rather it is as if the rich sat down and played a quick game of MAD where they realized they needed a controlled outlet to realize the informative value and entertainment value of journalism but not have chaotic reporting where the message cannot be controlled. What's more journalism offers what I would call auditor-caused moral hazard--if the auditor doesn't catch it or correct it, then it must be okay. That is a useful if unintentional purpose.

Of course there was not some secret meeting on Jekyll Island where journalism was launched, and the early twentieth century's muckraking shows how different the market for journalism can play out than what the rich and powerful might otherwise like. However, it was some of the rich and powerful on the production side of muckraking. So, no; journalism was not centrally planned or created in the last 200 years. It is a very long-run emergent order. Yet being emergent does not preclude it from my game theory theory or isolate it from powerful guiding influences. I think that my theory well explains how it was nurtured and shaped. Or perhaps captured is the better term. When journalism emerges as powerful enough to threaten the elite, the elite appropriate it for themselves.

With some ebb and flow between a more pure journalism and a more controlled journalism, this all is going along nicely until the Internet comes along. Then chaos. The Internet causes major disruptions to this order by commoditizing the tools of journalism with blogging, smartphones, et al. flattening the business model. The elite did not have this in mind. If the journalists are "us", and all of us at that, then we, elites and all, have to be more honest. We can't control the message or information--at least that control is very greatly weakened. Journalism before served a purpose to tell a story, a version of the truth, to the masses as a few saw fit. Now journalism is telling many stories, many versions of the truth including many with higher truth value than before, to varying numbers of consumers as many see fit. And it is deeper than that. The story isn't so one directional. It is more and more a conversation.

The quickest way to wreck a game theory optimal solution is to change a premise. The Internet is just such a change to the game theoretic outcome that journalism had been for so long.

Wednesday, March 6, 2013

Who benefits from recruiting deregulation?

The media tend to follow conventional wisdom. Sports analysis is much so the rule than the exception. Here is case in point #342 . . .

CBS Sports is guilty in this case by failing to connect the dots to the obvious--that Alabama has more to lose than gain in the NCAA's new recruiting deregulation. 

Here is the big surprise:
But, according to al.com, Saban told Birmingham's Over the Mountain Touchdown Club at its Monday banquet that he didn't think the changes were necessary.
"I'm kind of happy with the system we have now," Saban said. "To use the idea that, 'We can't monitor it, so why don't we just make it legal?' I don't buy into that at all. It's like saying, 'People are driving too fast. We can't enforce the speed limit, so let's just take the signs down and let everyone go as fast as they want.'"
No kidding he's "kind of happy with the system we have now". So was Pan Am in 1974 happy with airline regulatory policy. Saban is effectively responding to the question should the NCAA change with, "No! I think you should stay the same wonderful person you are today." Unfortunately, this change is just a change in clothes. Real reform will be met with much more kicking and screaming.

CBS is also guilty of confusing success with wealth and power:
It has been widely speculated--including by [Georgia athletic director Greg] McGarity himself--that wealthy programs like Alabama would gain a competitive advantage over less-wealthy schools by employing whole staffs of recruiters.
Georgia is a "wealthy" program. Georgia is on the same side of this as Alabama. It is the Georgia Techs and Boise States of the world who stand the most to gain from NCAA ease up.

Looking to the example of OU and OSU, it takes one wealthy donor to elevate a program to much higher plateaus. But staying there is made very difficult in a world where competition is limited in scope and scale. By removing certain dimensions of differentiation and competitive advantage (that is by having stringent recruiting rules as there are currently), the NCAA helps Alabama, et al.

Thursday, August 23, 2012

Getting political compromise through a new election format

It is commonly said that we live in an atypically divisive era in politics characterized by extreme partisanship and bitter, hostile stalemates. I have my doubts about how atypical this era really is or how bad the consequences really are from it. George Will seems to agree (specifically around the 13 minute mark).

But let's assume too little compromise is a colossal impediment to competent and effective (and desirable) government. What might be a solution? Perhaps a change in how the ruling elite come into power. One not too well fleshed out idea is as follows below. Think about it from a game theoretic perspective with the idea that we are trying to get reliably constructive political compromise between the two major parties. A key assumption is that the public strongly prefers compromise. I'll make the further ridiculous assumption that only the two major parties versions of the same party (Republicans and Democrats) are in contention for election (i.e., I'll ignore all independent parties just like the media does).

Every five years the party out of office makes a decision. It can either:

  1. Choose to hold the presidency for certain for two years followed by the opposing party holding office for certain for the next three years, or
  2. Choose to have an election with the winner holding the presidency for five years.
Here is my theory on why this brings about compromise. For the party in office in years three, four, and five, being too uncompromising allows the opposing party to choose an election which the opposing party is most likely to win. If that party during it's five-year reign is too uncompromising, an election is sure to follow along with another flip in who holds government. It seems to me that the equilibrium is a revolving two-year, three-year rotation kept alive by the party in power working hard to sell the public on how constructively compromising they are. Of course this is oversimplifying and of course this would just lead to bad politics on steroids as the uncertainty was removed for the political class. My belief is that these guys fighting is a lot better for government than these guys getting along. But I think it is a fun thought exercise, nonetheless.