Operationalizing HDB Balloting with Multiple Selections

Some thoughts:

What kind of housing comfortably houses 1 person? What kind of housing comfortably houses 2 people? What kind of housing comfortably houses 2+1? And 2+2? How about 2+3? Is 2+4 even advisable given it is public housing?

These correspond, perhaps, to five flat types: shoebox, 2 room, 3 room, 4 room, and "actual" 5 room flats. (Where number of "bedrooms" = number of "rooms" - 1.) But what about those that need a little more space but not that much more and cannot afford to pay for that little bit of extra space? What if low income households whose affordability range is at about a house for 2 want to have 1 kid but can't afford going all the way to a 3rm flat. A 2rm with a larger living room perhaps.

Suppose we add 2 shoebox variants, 2rm+, 3rm+, 4rm+, actual 5rm+ for a new total of 11 flat types. Taking the shoeboxes out (shoeboxes relate more to "lifestyle choice" than "income"), we have 8 flat types that allows for better pegging to income level due to less "sandwiching".

Now there is a new problem of how to handle balloting since the number of flats per type becomes much smaller. It is no longer practical to ask for applicants to indicate only a single flat type. The reality is, it probably is more sensible to ask applicants to indicate 2 to 4 choices (in the same development) in order of preference. How to implement the balloting process now becomes the problem.

Given a few ballot orders and the preferences of balloters, how do we allocate flats well. Can we obtain an allocation where no two balloters would be willing to perform mutual swaps of numbers for one or more of their choices? (The "no-envy" condition.)

Let me describe a simple process that provides a result that satisfies that "no-envy" condition.

1. Balloters get numbers for all the flats types that they have indicated a preference for. (Recall these are in the same development.)
2. Pairs of balloters are compared in a random order to make them happier by mutual swaps of their ballot numbers. At the end of this process, the "no envy" condition will be satisfied.

At this point, we can stop and have people make appointments to select flats in order of ballot number. (These appointments for the same development should be approximately concurrent.) Balloters should be instructed that missing or cancelling an appointment is equivalent to giving up a number, so they may gamble on others not selecting flats at their own risk. (The selection of a flat cancels all other appointments.) If this option is selected, we are done.

(If there are theoretical questions on the resulting ballot numbers I think I can answer them. Like given a set of ballot orders and preferences, is the "no envy" allocation generated from this random process unique? The answer to that one is no due to the random comparison order. So it is not "optimal" in a sense, though "optimal" is hard to quantify rigorously due to the number of conflicting interests. We'll leave theory to another day, if there is interest.)

On the other hand, if it is desirable to pare down the number of appointments on paper, it can be done, but the algorithm I can think of is not so rigorous. (A better way is to incentivize people to give up the appointments they do not really need through a small price discount, say $500 per appointment dropped.)

In any event, it is not hard to give those balloting for flats more choices. Why can't someone's application read:

1. Geylang (4 rm)
2. Kallang (4 rm)
3. Hougang (4 rm)

It is just a matter of getting the math sort of right. Which means incentive compatibility, which I haven't explored.

My house shall be called the house of prayer; but ye have made it a den of thieves

And Jesus went into the temple of God, and cast out all of them who sold and bought in the temple, and overthrew the tables of the moneychangers, and the seats of them that sold doves,

And said unto them, It is written, My house shall be called the house of prayer; but ye have made it a den of thieves.

— Matthew 21:12-13 (KJV)

Christ Driving the Money Changers from the Temple by El Greco
(Source: Wikimedia Commons)

I was discussing the City Harvest Church (CHC) case with a colleague who is a non-Christian with a particular distaste for CHC. His view is that if one is trying to evangelize, one should at least know enough about the subject matter to answer simple questions. He said that the best answer he got out of CHC's "evangelists" was "I see you are very interested in this, why don't you come down and there will be people who will be able to discuss this further with you." More quick wit than substantive content, he declined.

I was pleasantly surprised that he was familiar with the above biblical anecdote which has resonated with me (for a long time). When I was much younger, I found it extremely distasteful how my church was a cesspool of discussion about stock trading, discussion about property, boasting of children's exam results with little mention of "God", "Jesus" or "The Holy Spirit" in the fellowship hall. Much later, I understood that these people were in church to network with other "English-speaking professionals" much like some boys go to church to meet girls. (Granted, it may have been a biased picture not representative of the whole, but it was a big enough segment, and thankfully, the youth ministry made up for that deficiency.) This childhood background has fueled my disdain for the zombies that lust for money (as opposed to chewy grey matter). These impressions, in turn, fuel my vehement distaste for the money grubbery that is CHC.

Since ancient times, those seeking money have understood that foot traffic is strongly correlated with commerce (location, location, location), just as today attendences are correlated with takings. This would be a great case study at the Harvard Business School with its low cost of customer acqusition (through a viral engine of growth), high retention rates by giving people what they want: "you will be wealthy" and "God is indeed Santa Claus" and effective cross selling to increase lifetime customer value.

There is much schadenfreude going around on this matter. Many people have written about this matter in the past days. Disgusting anecdotes of coercion to "give" have emerged. Criticism of teachings at CHC, having been around for an even longer time, are receiving a fresh infusion of readership. (I am pleased. *chuckles*)

On a seperate note, the level of brainwashing is quite clear noting that some CHC members "remain loyal" in spite of clear signs of aspiritual greed (e.g.: giving a "discount" of $770k and then recovering that discount from some other fund). We should bear in mind that the amounts we are talking about are not peanuts, we're talking about the entire bag. Those people... it will take some time...

Goodbye Libertarianism

I'm giving up libertarianism. Or rather, I've long given up on it and am declaring it now. The fact is, some people by virtue of pure luck are gifted with resources that others are not. Those with few resources will need help from those with plenty. I find it extremely fishy that most libertarians have coincidentally, by the uncaring lottery of the fates, been born into an unearned bounty.

The practice of libertarianism is fraught with contradictions. The libertarian businessman does not want to be taxed, but still desires the trained work force built up by public expenditure on education. One cannot just pick and choose to be free of obligations in some areas and to have others obligated to provide for one in others.

Aristotle said that a creature that is unable to live in society or has no need because he is sufficient unto himself must be either a beast or a god. Since we all are clearly not gods and hope not to be beasts, we need each other. The libertarian would not disagree with this and state that we should be free to associate and treat with each other in mutually acceptable ways. The picture that this paints is of an idyllic commune where apples are traded for eggs and a musician is paid for his craft with a pint of homebrew. But modern reality is not so simple. Can libertarian ideas support a complex economy? In my mind, no, but I'm not sure if that is actually the case. (I've not been keeping up with my reading.)

Applying libertarianism to national defence is a recipe for market failure. "Libertarian practice" in this case would propose that individuals to hire defence service providers from a free market. Those who cannot afford this service or for whom this service would constitute "non-cost effective" overhead will have to go without. So those with few belongings would be open to expropriation by those who do not subscribe to the enlightened libertarian philosophy. But if everyone would follow the libertarian creed of not curtailing the freedoms of others, there would be no need for national defence. So "libertarian practice" is basically irrelevant to national defence.

(Digression: The Roman system of conscription kept Rome strong until that system broke down. From the beginning, only land owning citizens were obliged to provide men and equipment for the military. This is very much consonant with the idea that you get what you give: your blood and your steel for the protection for your property. We need more "you get what you give" in public policy.)

What about education? The free market will leave a legion of poorly educated unwashed masses angry at the unfairness of their fates and directing their fury at the enlightened libertarian lords who might be sipping champagne while pontificating on the finer points of libertarian philosophy. That will not end well.

So does it work? It doesn't look that way. Am I knocking over a straw man? Probably. Or do I just lack a sufficient understanding of the intricacies of libertarianism. Even more likely. But I guess by and large people are pragmatic with a pragmatism will be seasoned by something between the antipodal tendencies to either "maximize one's utility" or to "be a blessing to the world". "Libertarianism" today simply smells too much of pragmatic self interest for my tastes.

Illegal Subletting and Deterrent Penalties

Illegal subletting of HDB flats should be punished. Severely. It is a violation of the spirit of public housing. The question is, what is the appropriate penalty in monetary terms?

This is the expected number of months of rent that an illegal subletter expects to get:

(1-p^12N)/(1-p)

where p is the probability of not getting caught in a given month and N is the rental life of the unit.

This expression may not quite look right, but I assure you it can be obtained by summing

Sum_{[k=0 to 12N-1]} (k+1) p^k(1-p)

which considers cases where an illegal subletter is caught and stops and

Sum_{[k=12N to ∞]} 12N p^k(1-p)

which corresponds to the case where the illegal subletter is not caught and obtains rentals for every month of the rental life of the unit. [As for why they are equal, I don't have any deep intuition beyond just working it out. I was so skeptical, I did the sum explicitly in Excel and did a comparison. It does check out.]

This, multiplied by the monthly rental, is the minimum fine that should be levied to make illegal subletters indifferent between obeying the law and trying their luck. Raising it a bit more would tip the scales in favour of the law.

Since the rental life of flats tend to be long, for any small probability of getting caught in any given month, the expected number of months of rental accrued is very high. For instance, if the probability of not getting caught in a given month is 0.995, then for a flat with a rental life of 20 years, the probability of not getting caught at all is about 0.3 (and the expected number of months of rent accrued is 139.94).

At a glance:

Expected Months of Rental Collected		Rental Life N (years)
		5	10	15	20
p	0.9975	55.7815	103.784	145.0924	180.6402
	0.995	51.9478	90.4027	118.8694	139.9422
	0.9925	48.4603	79.3076	98.9434	111.4425
	0.99	45.2843	70.062	83.6192	91.0371
	0.9875	42.3889	62.3175	71.6868	76.0916
	0.985	39.7462	55.796	62.277	64.8941
	0.9825	37.3314	50.2742	54.7615	56.3172
	0.98	35.1223	45.5731	48.6828	49.6081
	0.9775	33.0989	41.5482	43.7051	44.2557
	0.975	31.2434	38.083	39.5803	39.9081
	0.9725	29.5396	35.083	36.1233	36.3185
	0.97	27.9731	32.4714	33.1947	33.311
	0.9675	26.5311	30.1855	30.6888	30.7582
	0.965	25.2019	28.174	28.5246	28.5659
	0.9625	23.9751	26.395	26.6392	26.6639
	0.96	22.8412	24.8136	24.9839	24.9986
	0.9575	21.7919	23.4011	23.5199	23.5287
	0.955	20.8194	22.1337	22.2166	22.2219
	0.9525	19.9171	20.9914	21.0493	21.0525
	0.95	19.0786	19.9576	19.998	19.9999

Probability of Non-detection		Rental Life N (years)
		5	10	15	20
p	0.9975	0.8605	0.7405	0.6373	0.5484
	0.995	0.7403	0.548	0.4057	0.3003
	0.9925	0.6365	0.4052	0.2579	0.1642
	0.99	0.5472	0.2994	0.1638	0.0896
	0.9875	0.4701	0.221	0.1039	0.0489
	0.985	0.4038	0.1631	0.0658	0.0266
	0.9825	0.3467	0.1202	0.0417	0.0144
	0.98	0.2976	0.0885	0.0263	7.84E-3
	0.9775	0.2553	0.0652	0.0166	4.25E-3
	0.975	0.2189	0.0479	0.0105	2.30E-3
	0.9725	0.1877	0.0352	6.61E-3	1.24E-3
	0.97	0.1608	0.0259	4.16E-3	6.69E-4
	0.9675	0.1377	0.019	2.61E-3	3.60E-4
	0.965	0.1179	0.0139	1.64E-3	1.93E-4
	0.9625	0.1009	0.0102	1.03E-3	1.04E-4
	0.96	0.0864	7.46E-3	6.44E-4	5.56E-5
	0.9575	0.0738	5.45E-3	4.03E-4	2.97E-5
	0.955	0.0631	3.98E-3	2.52E-4	1.59E-5
	0.9525	0.0539	2.91E-3	1.57E-4	8.46E-6
	0.95	0.0461	2.12E-3	9.78E-5	4.50E-6

To use these tables, one might first make a ballpark estimate of the probability of an illegal subletter never getting caught given he/she illegally rents out part of his/her flat for some number of years. Using the second table, a value for p can be estimated. Then the first table can be used to identify the right ballpark of a deterrent fine.

In any event, all this tells us that since it is very unlikely to ever get caught, the rental that an illegal subletter expects to accrue is extremely high. Therefore, unless there are stiff penalties such as large enough fines or repossession of the flat by HDB, illegal subletters will continue to ply their trade.

Creating a Support Structure for the Poor

I just read The Malay Underclass, an essay by some final year students from NTU about the socio-economic challenges facing lower income Malays.

(Actually, I realize I forgot to post this from some time ago.)

I believe that we can provide an additional support structure for low-income families. Let me describe what I have in mind. It all begins with the schools. I propose that primary and secondary schools provide additional tuition to kids from low-income families for most days of the school week (all for primary school kids). Meals should be provided (lunch and dinner). This allows the parents to work to support their families while their kids are under supervision. For the older kids (sec 1 and above), they should not be going through "tuition" every day, but rather, helping out at the sessions for the younger children.

Thus, kids from low-income families will be learning under some supervision and learning responsibility. The younger ones will have role models to look up to. Given this, it is far more likely that these children will be able to achieve better educational outcomes and learn some life skills that will stand them in good stead when it comes to tertiary education and the working world. In addition, those who are going through tertiary education should volunteer a few days a month to help out as well. I think of this as a socially meaningful form of "national service", but one where Kids first receive "full time" care and then come back as "reservists" to pay it forward. Furthermore, each kid gets a concrete sense that he/she is doing good for someone else. (To reinforce this, the parents of kids under full time care should be asked to attend a biannual ceremony to thank the teachers and students who have given up time and energy to help out in the program.)

Perhaps with programs like that in place, we can provide better and more effective support for low income families. In time, hopefully the program will no longer be necessary. Eventually only being preserved in the fond memories of graduates of the program who remember how their seniors paid it forward.

Ramblings on "Capabilities" and Aggression

It is somewhat interesting to note that the Roman Empire had little or no naval capability until the beginnning of the second phase of the First Punic War, which was marked precisely by the build up of a non-trivial naval force. Circular and somewhat uninformative definition aside, the Romans were extremely pragmatic in their military build up, especially given that its military consisted mainly the upper crust of Roman society who probably would not have liked to be assigned command of forces with no prospect of prestige through victory. Prior to battling Carthage across the ocean, Roman wars were land based and did not necessitate the use of naval power.

(Disclaimer: These are musings of a half-awake engineer on the way to work. I have not read Clausewitz or any military treatises and am not at all familiar with "the literature" in so far as it pertains to this.)

This interesting tidbit led me to think about the "capability" thought revolution in militaries around the world. It seems to me that almost every capability that people speak of are damage inflicting or coordinating. It seems that defensive capabilities such as detection and recovery (under a given damage loading) are a bit of a second thought. Perhaps the popularity of discussing "capabilities" began in the Cold War's era of deterrence where game theoretic response matching was the calculus of choice. The utility/benefit functions used naturally related to the amount of damage one could inflict on a foe and how much that foe might inflict on one. Those functions were typically dominantly based on (offensive) capabilities with little consideration of those of the defensive sort. This is the narrative that arises from the records of recorded discussions on the "first strike" and "second strike" capabilities of both sides and how they generated the uneasy equilibrium.

The view of a military "capability" as an offensive one by default is interesting in view of the fact that it was a defensive capability that won the Cold War for the USA. By largely neutralizing Soviet strike capabilities, the Soviet Union was left naked and with the two options of investing heavily in strike or investing heavily defence. The lack of economic capacity of the Soviet union and the pursuit of heavy investment... you know the rest.

It strikes me that the synonymous relationship of "capability" and "strike" is a manifestation of the aggressive tendencies of a military caste (or those with warrior pretensions). However, we should be aware of the historical record and the need for both a spear and a shield. Thankfully, there are those in Singapore who are interested in "resilience". I shall not talk about where we are at, however. (I don't even pretend to have a complete picture.) My own interest in the topic are in measurement and my view of may be summarized as comprising of enemy action, impact on resources, their reallocation to support "capabilities" and the corresponding impact on the performance of those "capabilities".

While we invest heavily in strike capabilities, we should be aware of the perennial defender's advantage (which can be neutralized by less tasteful forms of warfare, that in turn would probably provoke a very heavy handed international response). The defender's advantage is precious and should be bolstered. For instance through the ability to bust out of a blockade (the modern day seige). Investment in a good defence requires far more investment in offence to overcome. (This differential is lessened in computer games to prevent too much turtling.)

It is at this point where I must conclude these ramblings. And quite abruptly.

Plastic Justice

The matter of wealthy plastic surgeon Woffles Wu "abetting" his employee, Kuan Kit Wah, to "provide false information to the police" so as to cover up two of Wu's speeding offences (in 2005 and 2006 respectively). To say that verdict and its explanation by the AGC does not sit well with me is a severe understatement.

Yesterday, in reaction to the AGC's statement, I wrote the following letter to the ST Forum:

I refer to the AGC's statement on the Woffles Wu case ("PP v Wu Tze Liang Woffles", AGC Press Release, 17 Jun 2012). To quote the ST report of that statement ("AGC releases statement on Woffles Wu case", 17 Jun 2012). The highlighted that it was Mr Kuan, not Dr Wu, who had given the false information to the police and that as well as the lack of payment or gratification to Mr Kuan were taken into consideration in the sentencing. This leads to important questions on the interpretation of information given to the traffic police.

After a speeding vehicle is detected, traffic police systems issue a summons to the owner of the vehicle. This creates a correspondence between the owner of the vehicle as well as the traffic police. In this case, the owner of the car would be Dr Wu. The Traffic Police should not be accepting information from anyone on the case other than the owner of the vehicle as they have no standing in the case. Therefore, information provided to the police on the case might be regarded as having been provided via Dr Wu. If this interpretation is correct, Dr Wu should be held responsible for both providing false information to the police and abetting Mr Kuan to assert the veracity of that false information. This would have implications for the proper sentence.

As a matter of public interest, the Traffic Police and AGC are requested to provide clarification on this question of interpretation.

This morning, I learnt some specifics of speeding summons. In summons issued to the owner of the vehicle, he/she is asked to declare whether he/she was the driver by checking or not checking off the following statement:

"I am the registered vehicle owner but not the driver of the said vehicle on the date, time and place of offence as stated in your letter. I hereby furnish the driver's particular(sic) as follows:"

Law Minister K Shanmugam has come out and provided an explanation for the verdict PP vs Wu case based on the explanation given by the AGC. He should have been aware, as a past Minister for Home Affairs and as a lawyer, that such a declaration by Wu would have had to be made and that it would mean that Wu indeed was providing information to the police on the identify of the driver. (Unless, of course, the law's interpretation of communications is vastly different.)

The convenient omission of this fact is highly suspect. Two alternatives are available: (i) the deliberate perversion of justice (perhaps to help a poor rich guy out) or (ii) incompetence (an "honest mistake"). (This is a real dichotomy and not a false one.) I will take the Minister at his word that it was not the case that Wu was spared a jail sentence because he’s rich.

On Effective Incentives at Universities

University faculty members have different profiles. Simplistically, there are (i) those focused on research and/or industrial collaboration, (ii) those who emphasize teaching, and (iii) some who blend the two in a relatively balanced ratio. Both the functions of (i) and (ii) are important, but the former is seen as the more glamorous among faculty members and university promotion boards and search committees. Coming from the perspective of the university as a tool to support a nation's sustained competitive advantage, teaching edges out research and industrial collaboration in importance.

To develop effective incentives, we have to be a little hard nosed and be willing to bruise a few egos. We must face the fact that the "university system" has used the inventions and discoveries of a few talented individuals to justify the "contemplative life" for manifold numbers of others. The proliferation of uninteresting journal articles and conference papers is but a symptom of this.

"Research" takes pole position in universities as search and promotion preferences make clear. Those with personal leanings towards teaching advanced subjects effectively are edged out of the faculty or are forced to do "research" that turns out to be uninteresting (and they probably never get tenure anyway).

In Singapore, government ownership of universities allows changes to be made to align incentives in universities with national economic objectives. One way is to allow all faculty members to do what they do best. There are two related ways of measuring performance: absolute and relative (rank order). Additionally, there are different metrics by which performance can be measured. For instance, (i) the research productivity-industrial grants ruler, (ii) the teaching evaluation-student performance (in later courses) ruler, and hybrid metrics. Faculty members should be evaluated on all measures in absolute terms, and also have his/her rank on each measure computed. Remuneration and promotion should be based on all those measures.

To give a sense of what I am alluding to, consider the following. In principle we want to reward the top ranked performers, but at the highest levels of academic research performance, rank means little, so all top tier researcher (by absolute performance) should be rewarded highly regardless of rank; rank should only come in at the "lower" tiers. This conduces to the creation of a group with many top tier researchers and encourages faculty to move into the top rung. On teaching, similar incentives should be in place. Appropriate performance measurement logic should be there to "determine" the "role" each faculty member has crafted for himself/herself and use only the appropriate performance metrics.

The illustration in the above paragraph may seem a bit sketchy, but should give a flavor of what I am thinking. Incentives should be there to encourage faculty members to perform at the highest levels of performance of research and/or teaching. Staff who are mediocre at both over a sustained period should be let go. The university system should not be a place where only the forms of research are aped and knowledge is purported to be transferred. It should be a place where research is done and knowledge is transferred effectively.

---

Postscript: I'm writing this while "stuck in Rome". My passport was stolen from my left pant pocket on a crowded train 4h before my flight. The embassy was closed, and the police report was not accepted as a valid document for traveling out of Europe. When I got in touch with MFA, and through them the local Singapore consulate, it turned out the Italian Honorary Consul General had died and consular authority was transferred to Geneva. I was stunned to hear that. It all made things more surreal. Even stranger was when, today, I got an SMS from DBS Cards telling me that "I" had charged $15xx.xx for a United Airlines flight from the Las Vegas, Nevada branch. Woo.