I.

Living together, humans exchange ideas.

Some of those ideas have staying power. Views concerning good and evil and right conduct have been around for millenia. Notions of individual freedom and equal rights have been around for centuries. Concepts of gender and racial equality, decades.

Ideas come in and out of fashion; some last longer than others. Not all of them are good, and sometimes we have to let them go.

Still, we expect people to stick to their beliefs: especially our leaders and people we depend on. It is destructive when leaders renege on important issues to suit their immediate needs.

At the same time, we don’t want people to feel like they must perform their beliefs under external pressure. As we change, our attitudes change, and our expression of those attitudes should be free to change with them.

We want freedom. We want stability. How do we balance self and society? If something is good, will it last? If something lasts, is it good?

II.

Since the end of World War II and the ushering in of the postmodern age, it has become the norm to challenge and disassemble the authorities of yesteryear. An idea which has been passed on for hundreds of years is of the same value as one freshly conceived that morning; it is our intellect, and nothing else, that arbitrates between them.

The deconstruction was a cultural breakthrough, but has left us more sensitive to dialectical tensions yet poorly-equipped to resolve them.

Ultimately, the postmodern vision has been a gift and a curse. We cannot hold ourselves right a priori and we must ultimately find a way to balance flexiblity of thought with a valuing of tradition. The ideal balance is one that allows an individual to change their mind, while at the same time creating some incentive to stick to one’s beliefs. We must find a way to embrace change without fearing destruction.

It is easy to speak in generalities; it is hard to put things into action. In an attempt at the latter, we will bring this balance into practice, as a demonstration and extension of this theory of preference graphs.

III.

To review the language of preference graphs, we an individual \(e\), who has preferences written as \((b,a)\) when \(e\) prefers \(a\) over \(b\). We can imagine \((b,a)\) as a preference, or arrow, from from \(b\) to \(a\).

Thusfar when aggregating preferences, all preferences are given a weight of 1. Now we introduce a new dimension to preferences: the authority of a preference, a variable weight defined as some function of the time \(t\) since \(e\) first expressed the preference \(p = (b,a)\).If \(p\) is an arbitrary preference and \(t_p\) is the time since that preference was first expressed, then the authority of \(p\) can be defined as:

The authority function is intentionally general; any function will do, and the choice of function will shape our intereptation of the “authority.” Using a monotonically-increasing function, like the logarithm, creates an authority curve which is intuitive and useful.

IV.

What happens when we incorporate time into applications of preference graphs? Assuming a monotonically-increasing authority function and rational, self-interested participants, we might expect the following.

1. Individuals are incentivized to register their preferences as early as possible. Assume that individuals would like their views to have the maximum impact on the group. In the context of an online application or service, this creates an valuable incentive to adopt the product as early as possible.

2. Individuals will change their preferences less frequently. If an individual changes their preference, the authority of that preference resets. If an individual then decided that their original preference was the right one, the preference resets again, and the accumulated authority of thier initial preference is lost. There is an incentive to get it right the first time.

3. Individuals will change their preference when their views truly change. There is no benefit to holding on to views one no longer agrees with: if an individual truly feels differently about an issue, then updating their preference will achieve the desired directional affect.

In summary, the addition of a time dimension to a preference-aggregation platform creates powerful incentives to both adopt the platform and to behave responsibly once on the platform. It is especially worth noting that the additional computational complexity associated with incorporating the time dimension is small: \(O(n)\). That so many positive effects emerge from a simple computation is highly suggestive.