A generalized meaning of "spam" is an unwanted internet message

If your post is deleted as spam/offensive, it means that members of the community think the post is a detriment to the site and that posting it on the site was sufficiently misguided that it should be penalized. This is the accepted definition of "spam" on MO. Your question was not about probability or about mathematics. I don't even think it was an economic question. It's a philosophical question, but it's unlikely to be a fruitful one. It's like somebody making up a precise quantification of "health" or some other intentionally vague concept. I can't help myself from illustratating the sorts of pointless discussion these things lead to: your definition of value has absolutely no bearing on my probability of survival, so the value it would assign to itself is zero.

If you don't agree with the MO community about what counts as mathematics, it will only frustrate everybody when you try to do mathematics with it. With that, I'll take Andy's advice and bow out.

You all know that in today's world when it comes to measure value, most people would use dollar as a unit measure. There are other units though all of which can be more or less exactly converted to each other. But it seems that there is apparently no internationally-agreed theoretically-defined unit of value.

So my question is whether such abstract unit of value was indeed defined in any theoretical paper, about which I do not know?

Below are some my considerations about the topic.

First, it should be noted that economists developed concepts of personal value, marginal value, exchange value etc. These all mostly depend on which subject is considered and in what circumstances, sometimes can be derived following certain procedures from each other and can be measured in the same units, so such plurality should not mislead us.

1. It is indeed possible to postulate a unit of value as a value of say, 1 kg of gold. This definition is rather old and useful, but becomes problematic when there is no gold available.

2. Marxists seem to postulate the value as a measure of labour needed to obtain the commodity in question. The problem here is how to measure the amount of labour. In human-hours? Very inexact and completely non-abstract. Besides has little correlation with market prices.

3. Initially I thought that it may be possible to postulate a unit of value as a value o commodities which increase pleasure or reduce suffering twofold. This definition seems rather universal, but has the same problem: how to measure suffering and pleasure?

4. So I came to the following possible definition: unit value is the value of commodities which increase probability of a positive outcome e-fold for the following unit of time. Since a common negative outcome for all people and animals is death, it is possible to define a unit value as the value of commodities, which increases the chance of survival e-fold for the following unit of time, without creating any additional pleasure or suffering. We can then take a limit with the unit of time going to zero and integrate. Let $p_0(t)$ is the distribution of probability of survival without the commodity and $p_1(t)$ is the distribution of probability of survival with the commodity. Let $(t_0,t_1)$ is the interval of time through which the commodity affects the probability of survival (with t=0 being the present moment). Then value of the commodity V would be

$$V=\int_{t_0}^{t_1} ({t_1-t+t_0})\log \frac{p_1(t)}{p_0(t)} dt$$

If we take another logarithm base we can simply get another unit of value, proportional to the previous one. Following this definition it is possible to derive other concepts such as marginal value, exchange value (as a market equilibrium of personal values) etc.

This definition, though does not take into account possible sufferings and pleasure some commodities can provide, for example, the value of a box of cigarettes would be negative. But if we assign certain value to pleasure we can overcome this difficulty. Such value may be assigned based on empiric data regarding exchange rate of say, cigarettes and a commodity that increases survival without providing any pleasure.

So, I would like to hear any suggestions to improve this definition and possibly pointing to an existing abstract definition of this kind.

As for your (perhaps rhetorical) question concerning whether a mathematical expression is or is not mathematics, I think it's important to distinguish 'language' and 'subject'. As I stated already, there are many questions I could write down in mathematical language, but which would not be necessarily mathematical questions. And I would certainly not ask them in MO, however interesting I personally think they are. You should not feel offended because your question was closed. It does not mean that the question is not interesting, just that the MO community (or those who voted down or voted to close the question, at least) concluded that the question was not appropriate to the site.