Cake cutting, Dutch auctions and chit funds

Last night at what started off as high tea but ended up as dinner (for me, at least), Baada and I shared a cake. The cake was delivered to our table along with a (rather sharp) knife. I used the knife to cut  the cake into two, and Baada chose one of the two pieces (inexplicably he chose the smaller one). That way, we had achieved the most efficient method of splitting a piece of cake between two people.

It has been an interesting mathematical problem as to how to split a piece of cake between three people, since the above algorithm doesn’t work. The problem has been solved, but is rather complicated with several cases, involving one person cutting a piece, the second person trimming it and offering it to the third, followed by further complications. I won’t bother describing it further here. And then you have the problem of extending the solution to N people sharing a piece of cake.

But then, there is an elegant solution, after all, which I found in Alex Bellos‘s excellent book Alex Through the Looking Glass a couple of days back. As Bellos describes,

One ingenious method invented in the 1960s, which can be used for any number of people, concerns a moving knife. The knife is positioned at the side of the cake and then moves very slowly across it. When someone shouts ‘STOP!’ the knife slices at that position. The person who shouted out receives the slice. The knife then continues for the remaining participants.

It is not hard to see how this works (it assumes that the players, unlike Baada last night, want the largest possible piece of cake while being fair). If you call too early, you end up with a smaller piece of cake than you’re entitled to, and so you wait. You call too late, and someone has already called for it. So with every player playing the optimal strategy, this moving knife strategy results in each person getting their fair share.

While reading this cake-cutting strategy, I got reminded of the Dutch auction. In such an auction, the house starts with a very high price, which drops slowly (represented by a clock, usually). And as the price drops, when one of the buyers is willing to pay the price at that moment, they bid for it, and the object gets sold at that price. While it is a “first price auction” and buyers may not disclose their true willingness to pay (in the hope of getting the item for a lower price), the advantage is that it’s quick, and hence used for auctioning things such as flowers.

It works the same way as the cake-cutting algorithm in that if there is a well-defined value for the object being auctioned (this is rarely the case in practice), it makes sense to bid exactly at the point when the price equals this well-defined value.

This method of cutting cakes and auctioning flowers is also similar to how chit funds work in India. In a chit fund, you have N people who invest money into a pot at N different points in time. Each time, the money thus collected is auctioned to the person who needs it the most, and the price of the auction is determined by the amount that the person is willing to “let go” of the maximum amount. This amount that is thus let go of is distributed to the other participants (with the house taking a commission).

This is exactly similar to the cake cutting case. Think about it!

So it is very interesting that a fundamental feature of Indian homegrown finance, the chit fund, draws from important concepts in maths and game theory. We’re truly great!

 

Days of the week in Bahasa

Most languages name  their days of the week after a single source, and this is usually consistent across languages. For example, the original Latin names for the days of the week came from “planets” – Sun, Moon, Mars, Mercury, Jupiter, Venus and Saturn respectively. And this got copied into various languages.

So the days of the week as we know in English are derived from the names of these planets or Gods representing them (Thor giving Thursday and so on). Indian names for the days of the week are direct translations of the Latin names. And some days have multiple names in Indian languages, all of which mean the same thing.

So you have Ravivara and Bhaanuvara and Adityavara, all of which refer to Sunday, and all of which precisely translate to “Sun day”. The more formal name for Thursday is “bRhaspativara” but more commonly referred to as “Guruvara”, with “Guru” being the more common name for bRhaspati. And so forth.

Based on this background, I found the names of the week in Bahasa Indonesia, which I observed from signboards (Bahasa uses Roman scripts, so one level of Rosetta stoning can happen from signboards), rather interesting.

The names are (starting with Sunday):
Minggu
Senin
Selasa
Rabu
Kamis
Jumat
Sabtu

Ok I got that from this link as I was writing, but what I got from signboards yesterday was the names of Friday, Saturday and Sunday (Jumat, Sabtu and Minggu respectively). And I found it fascinating since it seems like they come from multiple sources.

So Jumat, it appears, is the day of prayer, or Juma. Considering that Indonesia is a Muslim-majority country (it’s not funny how empty restaurants are during lunch nowadays, since it’s Ramzan), naming Friday as “the day of prayer”, using the Muslim word for prayer, is absolutely logical.

Sabtu for Saturday is obviously derived from “Sabbath” – another day of prayer but for a different religion (Judaism). It looks like it’s derived from European names for Saturday – Saturday in Spanish is Sabado, for instance. So actually, in this case we are seeing a wider adoption of naming the day of week after its religious significance than the associated planet.

And Minggu, it appears, is diminutive for Domingo, the Spanish and Portuguese word for Sunday (and perhaps there are similar names in other European languages). And it appears that “Domingo” has nothing to do with the Sun, but instead is derived from Latin for “God’s day” (since Sunday is the day of the Christian God, who famously took rest on that day).

So it’s interesting that Bahasa has names for three days of the week which are not based on the planets, but on different versions of “God’s day”, with multiple origins among them! Or rather, that Bahasa has three “God’s day”s, with each referring to a different god.

I’m reminded of this store that existed a long time back close to where I currently live. It was called “yellAdEvarakRpe stores” (store with the grace of all gods).

New line of business

I’m considering a new line of business. This is basically advising startups on option valuation and how to account for different conditions and optionalities that venture capitalists put in in term-sheets.

Aswath Damodaran has an extremely interesting piece on valuation of the so-called “unicorns” and how such valuations are inflated on account of optionality in favour of investors. He takes a stab at valuing such optionality, but I think there’s scope for going deeper and helping companies figure out the valuations in each individual case. Money quote from the piece:

As an outsider with an interest in valuation, I find venture capital deals to be jaw-droppingly complex and not always intuitive, and I am not sure whether this is by design, or by accident. When it comes to investor protection, the stories that I read for the most part are framed as warnings to owners about “vulture capital” investors who will use these protection clauses to strip founders of their ownership rights. I think the story is a far more complex one, where both investors and owners see benefits in these arrangements, and where both can expose themselves to dangers, if they over reach.

Do you think this is a good line of business to get into? Will startups be willing to pay for a service that allows founders to get value for money for the equity they are giving away? Or will they be so focussed on execution that trifles such as a change in valuation by a few percentage points don’t matter to them any more?

And what are the odds that if I get into this business and do a good job of it, a VC will want to hire me just so that I stop damaging their carefully designed ratchets?

Slider design

Not often that I comment on User Interface, but this has a quantitative aspect to it, so I thought I’ll write about it. Basically it’s with the use of sliders on websites that you move around to determine an amount or a limit.

More specifically, I’m in the process of planning an extended weekend in Bali next month (the wife is going to be based in Jakarta for two months starting this weekend), and checking out sites such as TripAdvisor and AirBnB for accommodation. This necessarily means using a slider to determine my maximum willingness to pay for a room.

The problem with such sliders is that they’re linear. So for example, on the Travelmob page where I’m looking for villas, the price per night varies from Rs. 650 to Rs. 65000, or a factor of 100. And the slider uses a linear scale. So considering that I consider about Rs. 3500 per night as my budget, in order to set that budget I have to move the right slider (my maximum willingness to pay) way over to the left, till it almost coincides with the left slider (which determines the minimum price). And considering the small distance between the two sliders, it is easy go wrong and not be precise on your limits. A rather frustrating experience!

Instead, if the slider were to use a logarithmic scale, then 6500 would be the midpoint (geometric average of minimum and maximum), and that would allow me to pull the slider to 3500 without much hassle, improving my experience!

But then I suspect the current poor design is by design – by making it hard for you to move sliders down to low prices, maybe they are nudging customers to go for higher priced rooms?

On a different note, while on the topic of sliders, there are “fin-tech” startups that determine whether you are good credit depending upon things like the amount of time you spend moving around a slider to determine how much money you want to borrow. Quoting from Sangeet’s blog:

As an example, most peer lending platforms have a slider allowing the borrower to decide what loan they would like to take. In an excellent whitepaper by Foundation Capital on the state of peer lending, Charles Moldow shares that  the longer a borrower spends moving the slider up and down (and hence, potentially, debating her ability to return the loan), the more likely is she to return the loan. Such correlations help platforms improve their ability to curate participants over time.

This slider also looks linear, rather than logarithmic! And so it goes.

Update

AirBnB actually uses a logarithmic slider! Whatay!

Dispassionate blogging and Wife Bonus

So I’ve figured out that the key to being a good and interesting blogger is to be able to look at things dispassionately and not let your value judgments crowd out your reasoning abilities. Of course, while saying this I’m assuming that I’m a reasonably good blogger (based on feedback, implicit and explicit, that I’ve received over the last decade, and given that I’m coming close to 2000 posts here).

So earlier this morning I was talking to a friend about long distance relationships and careers and marriages and responsibility sharing, and he sent me a link to this rather fascinating concept called the “wife bonus“. The money paragraph:

A wife bonus, I was told, might be hammered out in a pre-nup or post-nup, and distributed on the basis of not only how well her husband’s fund had done but her own performance — how well she managed the home budget, whether the kids got into a “good” school — the same way their husbands were rewarded at investment banks. In turn these bonuses were a ticket to a modicum of financial independence and participation in a social sphere where you don’t just go to lunch, you buy a $10,000 table at the benefit luncheon a friend is hosting.

So I responded that this looks like a rather interesting concept, and started my own analysis of why this works and these bonuses have been structured in the fashion that they have. Unfortunately the discussion went nowhere.

Because my friend who sent me the link found the concept disgusting and abhorrent and demeaning to women, and he was fascinated that I had managed to actually analyse it without feeling the same kind of emotions. As I write this, the conversation continues (as the old Coffy Bite ad went). Ok I googled and found that it’s actually “the argument continues”. Here is the ad:

So based on this one data point, and a few other data points from my and my wife’s blogging past, I figured out that such dispassionate analysis (I’ll present my dispassionate analysis on wife bonuses later in the post) is key if you are to be a good blogger. Because such dispassion allows you to not get swayed by the emotion or repugnancy of a concept, and instead analyse it to its full merit.

In this case you start wondering why these highly qualified women don’t work, but are “interested in art”. You start wondering about how a family’s finances would work if the qualified wife doesn’t work. You start wondering who controls the budgets, and considering that one half is not contributing financially, how stable such marriages are.

So my hypothesis, which I’ve never bothered to test, is that people who have access to funds but don’t have an independent source of income are less careful about spending it optimally than those who have access to funds on account of their own sources of income. To be less politically correct, the hypothesis is that housewives (and househusbands, to be more politically correct) are less careful about their money than people who work.

So now if you have a spouse with no independent income source, but want to make sure she has access to sufficient funds while making sure she doesn’t fritter away the wealth, the best way of achieving this is to ringfence the money under her control. Which means that giving her control of your bank account is not optimal, but creating a separate purse which is under her control is superior! And thus you create what can be classified as a “wife bonus”. As simple as that.

Now I realise many of my readers will find this blog post repugnant, for it is not politically correct, and they will allow their emotions to take over and brand me as a misogynist or a chauvinist or whatever else. All because I looked at an existing phenomenon logically without attaching a value judgment to it. And by doing so, they deny themselves the opportunity of reading my analysis. But there are others who are happy that there is someone doing this dispassionate analysis, and they will like such analysis. And my blog popularity grows on that front.

My wife has been blogging heavily through her life in business school (coincidentally I started blogging a decade ago when I was in business school; and we met each other through LiveJournal), and has already got to the stage where her professors read her blog. And while a lot of her classmates read her blog, there are some who have problems with it, that she writes dispassionately about everything without value judgments.

Anyway, I sent her the NYTimes piece on the wife bonus. She replied that she also wants one now!

Investing in dabbil-dabbi startups

So the wife has come up with this new concept – “dabbil-dabbi startups“. Check out this scene from yedurmane ganDa, pakkadmane henDthi where miser Shashikumar is looking for the money that he has stored inside a series of boxes (watch at 3:48 here).

So the wife’s point is that startups nowadays are not adding value by themselves but instead simply offering an additional layer around an already existing product/idea. This, she says is similar to Shashikumar in the above scene putting one box inside the other – basically no real value is added.

I take this analogy further, perhaps distorting it in the process, like any analogy taken too far. Basically in the above scene, Shashikumar, after opening all the boxes inside boxes, retrieves money from the innermost box and rhetorically cribs that the money hasn’t grown.

Similarly, when an investor invests in a “dabbil-dabbi” startup, his money meets the same fate as Shashikumar’s in the movie – there is no growth!

So think twice before investing in a dabbil-dabbi startup.

Splitting BBMP and gerrymandering ToK

Kannada organisations have argued against splitting of the Bruhat Bengaluru Mahanagara Palike (BBMP), the civic agency that is supposed to govern Bangalore, arguing that a three-way-split of the municipal corporation, as has been proposed, will lead to “non-Kannadiga mayors” for some of the newly created corporations, and hence this is an “anti-Kannada” move. In a funny twist, the Chief Minister himself has had to make a statement that the split won’t lead to “Telugu and Tamil mayors”.

A couple of months back, Thejaswi Udupa had written this tongue-in-cheek post on the geopolitics of Bangalore, for April Fool’s Day on Takshashila’s Logos blog. The Business Standard picked it up and published it as an Op-Ed the next day. The reason the piece matters is that it introduces the larger public to the wonderful phrase ToK. Quoting,

The largest of disputed territories in Bangalore is that of ToK. Tamil occupied Karnataka. These are large swathes of interconnected parcels of land in the South-Eastern quadrant of Bangalore. ToK’s existence is mostly under the radar, and people notice it only when the census figures come in once a decade with its linguistic break-ups, and suddenly people realise that nearly 25% of Bangalore’s population is Tamil. However, there are many who believe that ToK stands for Telugu owned Karnataka, as most of the land here is owned by Telugu landlords.

So basically the concern of the Kannada organisations is that when Bangalore is split ToK (however you may define it) will become an independent city. While some people might consider it a good thing in a “ok those buggers are not in our city any more” sort of way, these organisations will see this as a loss of territory, and consequently as a loss of power. So this is a genuine problem.

While this might be a genuine problem, the fact is that there is a “genuine” solution to this problem. We had seen last month about how Bangalore city is so badly gerrymandered in terms of splitting its assembly constituencies. For example, my constituency (Padmanabhanagar) looks like a dancing hen. To refresh your memory, this is what Bangalore’s assembly constituencies look like:

So if assembly constituencies are so badly gerrymandered, what prevents us from gerrymandering the municipal corporations? And there is further precedence to this – there are primarily three Parliamentary constituencies in Bangalore, and it is not hard to argue that they have been gerrymandered in a similar manner.

It all finally comes down to the mechanics of how we split the city. If the city is cut into three by drawing North-South lines (creating “Bangalore East”, “Bangalore West” and “Bangalore”), we have a problem, since the Bangalore East thus created will largely coincide with ToK, and we might end up with non-Kannadiga mayors there, as the Kannada organisations fear.

However, considering that Bangalore is being split for purely administrative efficiencies, and for no real cultural reasons, there is no reason we need to split the city in that way. All we need to do is to draw the lines in an East-West fashion, as we have done with our Parliamentary constituencies, giving us a “Bangalore North”, “Bangalore Central” and “Bangalore South”. A split like this, well done and well gerrymandered, will ensure that ToK is split evenly into the three new corporations, and all will remain under the control of the Kannadigas.

So the Kannada organisations don’t need to fear the split. Solution exists. Only thing they need to fear is the way the split is implemented. And with precedence (parliamentary gerrymandering) on their side, they really have nothing to fear!

Acknowledgements

Thanks to Varun Shenoy for the discussions leading up to this post