Jul 012015

Read the Paper

Especially in urban areas, two locations may be quite close geographically but difficult to travel between. I wondered whether one could create a map where, instead of physical distances, points are arranged according to some sort of travel-time between them. This would be useful for many purposes.

Unfortunately, such a mapping is mathematically impossible in general (for topological reasons). But so is a true map of the Earth, hence the need for Mercator or other projections. The first step in constructing a useful visualization is to define an appropriate Travel-Time metric function. Navigation systems frequently compute point-to-point values, but they are not bound by the need to maintain a consistent set of Travel Times between all points. That is our challenge — to construct a Travel Time metric.

Read Paper

Jul 012015

Read the Paper

This is a scary piece in which I analyze precisely how many voters would be required to trigger a Constitutional Convention and ratify any amendments it proposes.  Because the 2/3 and 3/4 requirements in the Constitution refer to the number of States involved, the smaller States have a disproportionate effect.  In Congress, the House counterbalances this — but for a Constitutional Convention, there is no such check.

Read Paper

Jan 182013

Inflation, Up Close and Personal

It often seems like the inflation figures touted by officials and economists have little connection with the real world.  There are a number of reasons for this, some technical and some political.  But there is a deeper problem than the means and motives for calculating any specific index.   The issue is that any aggregate number is likely to deviate significantly from one’s personal experience.  Each of us saves for different reasons and spends in different ways.  Without taking these specific choices into account, we cannot accurately represent or protect against the inflation that we individually encounter.  This paper elaborates on this idea and explains how each of us can identify the relevant components of inflation, and best hedge our savings.

Read Article


Feb 122012

Taxes necessarily are unpopular. They represent an economic burden and do not yield obvious benefits. Though some make a show of embracing their civic duty, few voluntarily would undertake to do so if given a choice. The criminal penalties attached to evasion and the substantial efforts at enforcement are evidence of this. Nonetheless, there is a tie between one’s sense of social responsibility and the palatability of taxes. A perception that our sacrifice benefits ourselves, our loved ones, and society as a whole can mitigate the pain it causes. Conversely, if our hard earned money vanishes into an opaque hole of possible waste and corruption, resentment is engendered.

The taxes paid by an individual represent a substantial sum to him, but a mere pittance to the government. If there is no accounting for this money, then it appears to have been squandered. This assumption is natural, as the government is known to be a notorious spendthrift. Nor does the publication of a voluminous, incomprehensible, and largely euphemistic budget lend transparency. Even if it were perfectly accurate, and every taxpayer troubled to read it, the human mind isn’t wired to accurately grasp the relationships between large numbers. Thirty thousand dollars in taxes is minuscule compared to a billion or ten billion or a hundred billion, and it makes little difference which of those quantities is involved. Therefore an effort to elicit confidence through a full disclosure of expenditures would be ill fated even if well intentioned. However it would serve to enforce accountability, and should be required in addition to any other measures employed. If nothing else, this would allow watchdog organizations to analyze government behavior and identify waste.

So how could we restore individual faith in the system of government expenditure? There is in fact a way to do so and encourage fiscal responsibility at the same time. Individuals like to know where their money went. A successful tactic of certain charities is to attach each donation to a specific child or benefit. A person feels more involved, is more likely to contribute, and is better satisfied with their contribution if it makes a tangible difference. We need to know that we aren’t wasting our money.

The pain of an involuntary contribution may be assuaged through a similar approach. It may even transform into pride. There will be individuals who remain resentful, just as there are those who do not donate to charity. And some people simply don’t like being forced to do anything. However the majority of taxpayers likely will feel better if they know precisely where their money went.

We propose that an exact disposition of each individual’s taxes be reported to him. At first glance, this may seem infeasible. Funds are drawn from pooled resources rather than attached to such specific revenue streams. However, what we suggest can be accomplished without any change in the way the government does business, and our reporting requirement would not prove onerous. The federal, state, and most local governments already meticulously account for expenses — even if they do not exhibit particular restraint in incurring them. They must do so for a variety of legal and regulatory reasons, and records generally exist even if not publicly available.

Individual tax contributions need only be linked to expenditures at the time of reporting, but this must be done consistently. To that end, expenses could be randomly matched with the taxes that paid for them. This could be done each February or March for the prior year. We simply require that each dollar of taxes collected be assigned to one and only one dollar spent and vice versa. If there is a surplus, then some taxpayers would receive an assignment of “surplus” and if there is a deficit then certain expenses will be assigned a non-tax source – such as borrowed money or a prior year’s surplus. If a taxpayer’s contribution has been marked as surplus, then his true assignment is deferred until such time as the surplus is spent (again using a lottery system for matching). If it covers a prior year’s deficit then it is matched against that year’s excess expenses. The point is that every dollar of taxpayer money eventually is matched against a real expense.

For example, one taxpayer’s report could read “10K toward the construction of 121 example plaza, New York”, or better still “3K used for the purchase of air conditioning units, 5K for ductwork, and 2K for electrical routing for work done at XXX and billed to YYY contracting on ZZZ date. Work completed on AAA date.” An individual receiving such a report would feel a sense of participation, accountability, and meaningful sacrifice.

It may seem that few people would feel pride in defraying the cost of mundane items, but such an objection is misguided. These are real expenses and represent a more comprehensible and personal form of involvement than does a tiny fraction of an abstract budget. If an expense would appear wasteful, pointless, or excessive, then it is appropriate to question it.

What of the pacifist whose money goes toward weapons or the religious individual whose taxes pay for programs that contravene his beliefs? It may seem unfair to potentially violate a taxpayer’s conscience by assigning him an unpalatable expense. But no exceptions should be made. Their money is being spent in the manner described. Whether their contribution is diluted or dedicated, they live in a society that violates their ideals and they should vote accordingly.

It is our belief that a feeling of involvement in the operation of government, along with the requisite increase in transparency, would alleviate much of the general perception of irresponsibility, excess, and unaccountability. An individual may object to his relative contribution, but the means of its use would no longer be inscrutable. This could go a long way toward restoring faith in our government.

Feb 102012

Read The Document

In most real situations, we must make decisions based on partial information. We should neither allow this uncertainty to prevent action or pretend to perfect certainty in taking action. Yet in one area with a great impact on an individual’s freedom and well-being we do just that. Judges and juries are required to return an all-or-nothing verdict of guilt. They may not use their experience, intelligence, and judgment to render a level of confidence rather than a mere binary choice.

I propose adopting a sentencing mechanism based on a probabilistic assessment of guilt or innocence. This allows jurists to better express their certainty or lack thereof than does our traditional all-or-nothing verdict. The natural place to reflect such an imputed degree of guilt is in the sentencing phase. I discuss the implications of such a system as well as certain issues with implementation.


Read Document

Feb 082012

The current popular notion of democracy is something to the effect of “the will of the people is effected through voting.” Though this is a far cry from the original meaning of the word or its various incarnations through history, let’s take it as our working definition. It certainly reflects the basic approach taken in the United States. Though often confounded by the public mind with a vague cultural notion of freedom, it only conforms to this when taken together with certain other principles — such as explicit protections of individual liberties.

This aside, let us consider the components necessary for democracy. To do so, we must make some supposition regarding the ability of an individual voter to render a decision. We assume that every voting individual, regardless of aptitude, is capable of determining their purpose in voting. We say “purpose” rather than “criterion” because we refer to a moral choice, what they hope to achieve by voting. This is far more basic and reliable than any specific set of issues or criteria. A person knows their value system, even if they can not or do not have the means of accurately expressing it. The desires to improve the country, foster religious tenets, create a certain type of society, support the weak, advance one’s own interest, protect a specific right, or promote cultural development cannot easily be manipulated or instilled. While it is possible to create a sense of urgency or attach specific issues or criteria to these values, one’s purpose itself is a reflection of that individual’s view of society and their relationship with it. To meaningfully participate in the democratic process, an individual must translate this purpose into particular votes in particular elections. Note that a purpose may embody a plurality of ideals rather than any specific one (such as in the examples above).

It is the function of democracy to proportionately reflect in our governance and society the individual purposes of the citizenry. A number of components are involved, any of whose absence undermines its ability to do so. While the consequent process may retain all the trappings of a democracy, it would not truly function as one. Though it could be argued that such imperfection is natural and speaks to the shortcomings of the participants rather than a failing of the institution itself, such a claim is misguided. Regardless of cause, if the people’s will is not accurately reflected then the society does not conform to our popular notion of a democracy. Whether another system would perform better is beyond our present consideration. We simply list certain key requirements for a democracy to function as we believe it should, and allow the reader to decide the extent to which our present society satisfies them.

Note that a particular government need not directly represents the interest of every citizen, but its formation and maintenance must meaningfully do so. In some loose sense this means that (1) the effect of a citizen is independent of who that citizen is, and (2) the opinion of a majority of citizens is reflected in the actions of the government. These are neither precise requirements nor ones satisfied in practice, particularly in representative democracies. However they reflect our vague cultural concept of democracy.

The following are the major components necessary for a democracy to function as we believe it should.


Once a voter has decided upon a set of positions that reflect their purpose, they must have a means of voting accordingly. There must be sufficient choice to allow an individual to embody those positions in their vote. Furthermore, the choice must be real. Marginal candidates with no chance of winning may be useful for registering an opinion, but they do not offer true participation in the election. If there are only two major candidates then the voter’s entire purpose must be reduced to a binary decision. Only if it happens to be reflected in one of the choices at hand would their view be expressible.

If there are two major candidates and they differ only on a few issues that are of no consequence to a particular individual, then that person cannot express his purpose by voting. For example if a voter feels very strongly about issue X, and both major candidates have the same opposing position on that issue, then he cannot make his will known in that election. It may be argued that the presence of small candidates serves exactly this purpose and that if sentiment is strong enough one could prevail. This is not born out by history. In a two party system, a voter is reduced to a binary choice between two bundled sets of positions. As a more extreme example, suppose there are several major issues and the candidates agree on one of them. Even if every single person in the country holds the opposite position on that issue, their will still cannot be effected through that election. If there were no other important issues, then one or the other candidate surely would take the popular position — or a third party candidate would do so and prevail. However in the presence of other issues, this need not be the case.

Finally, there must be some reason to believe that the actions of a candidate once elected will reflect their proclaimed positions. Otherwise, it will be years before the voter can penalize them. Without such an assurance — and history certainly does not offer it — a nominal choice may not be a real one. The people then acts the part of a general who cannot move his troops, however much he may threaten or cajole them.


A well-intentioned individual must have a way of locating and obtaining information whose accuracy is not in question or, if uncertain in nature, is suitably qualified. Voters must have access to accurate and sufficient information. In order to translate their purpose into a vote, an individual must be able to determine the choices available and what they actually entail. Moreover, he must be able to determine the relative importance of different issues in effecting his purpose. Fear mongering, inaccurate statistics, and general misinformation could lead him to believe that a particular issue ‘X’ is of greater import than it truly is. Instead of focusing on other issues ‘Y’ and ‘Z’ which are more germaine to his purpose, he may believe that dealing with issue ‘X’ is the most important step toward it. Similarly, if the views of candidates are obfuscated or misrepresented or the significance of events is disproportionately represented, an accurate translation of his purpose into a vote may be denied a person. Even a perfectly rational and capable voter cannot make a suitable decision in the absence of information or in the presence of inaccurate information. This said, not every vehicle should be expected to provide such information. If a person prefers to listen to a news station that reports with a particular bias, that is not the fault of the information provider — unless it does so subtly and pretends otherwise.


A voter must have the intelligence, critical reasoning, motivation, and general wherewithal to seek out accurate information, detect propaganda or advertising, and make an informed decision. Their perceived interest must coincide with their true interest, and their purpose be accurately represented in the choice they make. It may seem that we are advocating the disenfrachisement of a segment of the population, individuals who — while failing to meet some high standard — have valid purposes of their own which they too have the right to express. This is not the case, nor is our standard artificial. We are merely identifying a necessary ingredient, not endorsing a particular path of action. Moreover, the argument that they would be deprived of a right is a specious one. Such individuals \emph{are} disenfranchised, whether or not they physically vote. They lack the ability to accurately express their purpose, and easily are misled, confused, or manipulated. At best they introduce noise, at worst their votes may systematically be exploited. A blind person may have a valid destination, but they cannot drive there.


Voters must be willing and able to participate. They cannot be blocked by bureaucratic, economic, legal, or practical obstacles — especially in a way that introduces a selection bias. Their votes must be accurately tallied and their decision implemented.


Not only must the structure of the democratic process treat all voters equally, their de facto influence must be equal. Depending on the nature of the voting system, certain participants may have no real influence even if the system as a whole treats them symmetrically. A simple example would be a nation consisting of four states with blocks of 3, 3, 2, and 1 votes, where each block must vote as a unit. Regardless of the pattern of voting, citizens in the state with a single vote can never affect the outcome. If that vote is flipped, the majority always remains unchanged. This particular topic is addressed in another paper.

There certainly are many other technical and procedural requirements. However those listed above are critical components that directly determine a voter’s ability to express their will through the democratic process. In their absence, voters could be thwarted, manipulated, misled, or confused. The purpose of democracy isn’t to tally votes, but to register the will of the people. Without the choice and tools to express this will, the people can have nothing meaningful to register.

Feb 072012

Read The Document

We often hear of cases that offend our sense of fairness — excessive sentences, minor crimes that are punished more severely than serious crimes, or two equivalent crimes that are punished very differently. Rather than attempt to solve a politically and legally intractable problem, we ask a more theoretical question: whether an individual can assign sentences in a way that seems reasonable and consistent to him.  Our system is a means of doing so.   We offer a simple algorithmic method that could be used by an individual or review board to ensure that sentences meet a common-sense standard of consistency and proportionality.

We intend to offer a less mathematical and more legally-oriented version of this article in the near future.


Read Document

Jan 262012

We should require that every bill be ratified by a second vote, one year after its original passage. It goes into effect as normal, but automatically expires if not ratified at the appropriate time.

Continue reading »