The Risk of Misinforming for Competing Messages

The Case Of Two Competing Messages: Two-To-One

The “two-to-one” topology is the simplest case for competing messages, describing two competing products. In this case, the client b_j receives two competing messages ¹D and ²D from two competing sources of information, describing two competing products ¹d and ²d and s/he has to choose which of the knowledge, acquired only by one of them, is suitable to solve her/his problem or to ignore both. In the business transaction context, the client purchases only one of the two products or does not purchase them at all. The case of two complementing messages is not discussed here, nevertheless that in reality the information describing one of the products can be used in assessing suitability of others.

The probability space describing this case extends the decision options described in Chapter 2.2. The client has the following options in making her/his decision:

• 1.

  choose ¹D: this message is useful, the client b_j solves her/his problem a_ij, the decision is correct, and the risk is ¹r_ij=0.

• 2.

  choose ¹D: this message is not useful, the client b_j doesn’t solve her/his problem a_ij, the decision is wrong, and the risk is ¹r_ij=1.

• 3.

  choose ²D: this message is useful, the client b_j solves her/his problem a_ij, the decision is correct, and the risk is ²r_ij=0.

• 4.

  choose ²D: this message is not useful, the client b_j doesn’t solve her/his problem a_ij, the decision is correct, and the risk ²r_ij=1

• 5.

  ignore both messages, but ¹D is useful and client b_j could have solved his problem a_ij if s/he has used the information from this message, while the message ²D doesn’t bring any useful information. The decision is wrong, the risks are ¹r_ij=1, and ²r_ij=0.

• 6.

  ignore both messages, but ¹D is useful and the client b_j could have solved his/her problem a_ij if s/he has used the information from this message; the message ²D also contains useful information. The decision is wrong, and the risks are ¹r_ij=2, and ²r_ij=1.

• 7.

  ignore both messages, but ²D is useful and client b_j could have solved his/her problem a_ij if s/he has used the information from this message, while the message ¹D doesn’t bring any useful information. The decision is wrong, and the risks are ¹r_ij=0 and ²r_ij=1.

• 8.

  ignore both messages, and both messages do not bring any useful information. The decision is correct, and the risks are ¹r_ij=0 and ²r_ij=0.