– Ralph Merkle
State of Satisfaction. Annually, all citizens are asked to rank the year just passed between 0 and 1 (inclusive).
If you wish, you can think of this as a poll of each citizen’s individual welfare, where 0 means the welfare of the citizen that year was the worst possible, and 1 is the best possible.
This scale provides no intellectual feedback on whether this or that person should be elected, or which bill should be adopted, or what policy is best: it is intended to provide information about one person’s state of satisfaction with the year that has just passed, and each individual citizen selects whatever value they please.
Summed over all citizens and divided by the number of citizens, this gives us an annual numerical metric between 0 and 1 inclusive, or a series of values each one of which summarizes the annual collective welfare of the entire populace for each year. An appropriately weighted sum of annual collective welfares, also extending indefinitely into the future, would then give us a “democratic collective welfare” metric.
More specifically, we can use ACWi, Annual Collective Welfare in year i, as measured by our direct annual poll, as our base. This year, we would measure ACW2016. Next year, we’d measure ACW2017. The year after, we’d measure ACW2018. And so on.
We then define DCWi, the Democratic Collective Welfare in year i, as 5% of ACWi + 95% DCWi+1. DCWi then gives us a value which depends on future values of
Effectively, DCWi lets us take a look into the future, with progressively declining weights over the next 20 or so years (1/20 = 0.05). In some sense, DCWi lets us look infinitely far into the future, but the weights become infinitely small, falling off exponentially the further into the future we go, with a characteristic decay time of ~20 years. That is,
DCWi = 0.05 × ACWi + 0.95 × DCWi+1
which can be expanded into:
DCWi = 0.05 × ACWi + 0.951 × 0.05 × ACWi+1 + 0.952 × 0.05 × ACWi+2 + 0.953 × 0.05 × ACWi+3 + …
We provide an example below of how we can trade DCWi, but the basic idea is that, as time passes, we can convert more and more of DCWi into ACWi. In year i, after the annual poll is taken, we can use the equation DCWi = 0.05 × ACWi + 0.95 × DCWi+1 to convert some fraction of DCWi into ACWi. The market for ACWi closes in year i and pays out. In this way, the “indefinite future” market for DCWi gradually becomes definite and convertible into cash.
This kind of “indefinite future” weights the near future more heavily than the far future, and uses a “discount rate” to determine the weighting. We might want to adopt a smaller discount rate, effectively making our prediction market pay more attention to the longer term future, perhaps the next 100 years, rather than the next decade or two. In this way, the “look ahead” of the prediction market can be adjusted. The smaller the discount rate, the longer the look ahead.
Paying attention to any finite period of time is, in some abstract sense, an incorrect strategy. That is, we only pay attention to the next day because we are insufficiently wise to deal with the next week. We only pay attention to the next week because we are unable to deal with the next month. We only pay attention to the next month because we are unable to deal with the next year. And so on. Ultimately, we want to deal with eternity, but we are not yet sufficiently wise. Any non-zero discount rate we choose is, therefore, a concession to our limited mental capacities.
Further, the concept of a “discount rate” is itself deeply flawed. Really, we are trying to model our growing uncertainty about the future by using a discount rate. But our uncertainty about the future is not uniform. Sometimes we can make statements about the very far future. To quote Stephen Hawking: “There are certain situations in which we think that we can make reliable predictions, and the future of the universe, on a very large scale, is one of them.”
At the same time, we can’t predict the roll of a dice even a few seconds into the future. Applying a uniform discount rate to the many events that might occur in our future seems like a heuristic that might be improved upon, if only we were clever enough.
That said, and acknowledging their limitations, at the moment adopting a discount rate seems like at least a plausible heuristic – until a better one comes along. If we think we’re going to be brighter in the future, we could adopt methods that allowed for setting the future discount rate to values progressively closer to zero. If the discount rate approached zero fast enough, the infinite future would have a significant weight in today’s considerations.
DCWi, Democratic Collective Welfare in year i, is our formalization of the less formal “collective welfare metric”. Either one can be replaced with the other. If you want to consider formally what is meant when we discuss evaluation of the collective welfare, we mean DCWi. If you want an informal description of DCWi, we mean the collective welfare.