Preventing Wrong Numbers
What might a phone company could do to prevent such problems? One possibility is to divide customers into two categories. Category A includes all customers, mostly commercial, who get a lot of phone calls from strangers. Category B includes all customers, mostly residential, who are likely to be bothered by wrong numbers. Assign numbers to the two groups in a way that makes it unlikely for an error in dialing a category A number to convert it into a category B number.
An alternative, starting with existing numbers, would be to calculate for each number its risk of being dialed by mistake. The calculation has three stages:
1. Research on what sort of errors people make in dialing--transposing, dialing an adjacent digit, and the like--and how likely they are.
2. For each phone number X, sum over all other numbers Yi the probability of misdialing X while trying to dial Yi times the number of calls per day that Yi currently receives.
3. Make a list of X's for which the sum is low--numbers unlikely to be misdialed--and offer them to customers at a premium price.