# Value of Information

28/03/2020

The value of information is a very slippery concept as information per se does not have any universal value. Its value is related to the person who uses it, when he uses it and for what he uses it. Any assessment of the value of information is therefore related to the value of the decision-making supported by such information.

For example consider two persons lost in the Sahara desert. One person has an adequate supply of drinking water (more than he could desire) and another has exhausted his supply. If one were to approach these two individuals with information about a drinking water well in the surrounding, such information will obviously have greater value for the one who has exhausted his water supply. For the one who is thirsty, this information is the most valuable piece of information for him at that point of time as it will determine if he will survive. If by chance the information reaches this thirsty person late and he dies of thirst, then the value of the same information becomes zero. So we can see that the same information can have different value for different people at different points in time. Hence, it will be fair to conclude that value of information is relative. There is no absolute value of information.

However, the normal mathematical and economical explanation of value of information suggests that if an event occurs whose expectation was low and information of its occurrence is known then such information is valuable. For example let us say that the reader of this text gets the information that an earthquake of 10.5 magnitude in the Richter scale is going to hit India and the epicenter of the earthquake will be the very spot on which he is located, then that information is more valuable to him than the information (say) that he has to pass his BCA exam to get into the MCA course. In the former case the information is more valuable to him as he is not expecting it but in the latter case he already knows the information with certainty and expects it fully and hence the value for such information is less. All market mechanisms work on this model of information. This has already been dealt with in the earlier chapter and as Eq.1 suggests, the value of information of an event is the negative logarithm of the probability of occurrence of the event. Therefore, the more unlikely the event the more its information value, if communicated correctly. This is also exhibited in our behavior as eons of evolutions have shaped us in a manner that we tend to attach more value to unlikely events. In a game setting for example, say a horse racing game, if the odds of a horse winning the race are more then the payoff for that horse is less. Similarly, if a stock in the stock market is likely to outperform the market then the price payoff for that stock is not high, but if a stock that is likely to underperforms, performs beyond expectation, then the price payoff become very high. Thus, we can that the issue of value of information is a complicated one.

#### Normative Value of Information

Marschak (1971) and McGuire (1972) made seminal contributions to this field of work. Decision theory has developed this concept further and the basic assumption is that we always have some preliminary information about the occurrence of events that are related to our decisions. This information or knowledge is represented by an a priori assignment of probability of occurrence to the event and hence a calculated payoff. The a priori probability might be objective or subjective as the case may be and with the knowledge of additional information the probabilities are modified resulting in a change in the expected payoffs. This approach is however, only good for theoretical discussions as its practical applicability is poor. The problem for such cases has to be highly structured, which is rarely the case in management.

#### Subjective Value of Information

It is the subject view of the information available. It is the subjective perception or impression of the information. This subjective value approach varies widely with individuals. In the subjective valuation of information, no probabilities are calculated. Subjective value of information is the person’s (receiver’s) comprehensive impression about the information content.