The algebra of adjacency patterns: Rees matrix semigroups with reversion

We establish a surprisingly close relationship between universal Horn classes of directed graphs and varieties generated by so-called adjacency semigroups which are Rees matrix semigroups over the trivial group with the unary operation of reversion. In particular, the lattice of subvarieties of the variety generated by adjacency semigroups that are regular unary semigroups is essentially the same as the lattice of universal Horn classes of reflexive directed graphs. A number of examples follow, including a limit variety of regular unary semigroups and finite unary semigroups with NP-hard variety membership problems.Comment: 30 pages, 9 figure

Using the stated preference technique for eliciting valuations: the role of the payment vehicle

At the core of the stated preference method is choice of payment vehicle. Since payment vehicle is an intrinsic characteristic of a good, the choice of payment vehicle will naturally impact on the valuation of the good. Typical payment vehicles applied in the context of health are income tax levies, out-of-pocket payments at the point of consumption or private health insurance premiums. Where out-of-pocket payments will elicit use value only, private health insurance premiums will also disclose option value, i.e. the utility of knowing that one has access to a healthcare service should one need it. Income tax levies will disclose what in this paper is referred to as citizen’s preferences, i.e. individual preferences that include use value, option value as well as (caring) externalities. This paper advocates that researchers design stated preference studies that encompass all relevant dimensions of value, and that serious thought is given to choice of payment vehicle. However, it is important to acknowledge that choice of payment vehicle has other potential implications for valuations. Payment vehicle and provider of services may be strongly linked in people’s minds. If respondents implicitly associate a specific type of provider with a certain type of payment vehicle, it is important that any misperception is corrected by way of a precise description of the good being valued. Further, a pertinent issue is the extent to which respondents ‘protest’ to the stated preference question and how we should deal with these ‘protesters’. No agreement currently exists about the procedure used to separate genuine zero values from protest values, nor about the treatment of protest responses in subsequent analyses. Beliefs are strongly associated with protesting, and exclusion of protest bids may therefore exclude individuals who have strong preferences for a payment vehicle. If it is acknowledged that payment vehicle is an intrinsic component of a good, exclusion of respondents who exhibit specific viewpoints may result in biased welfare estimates. Yet another issue is the presence of self-consciousness amongst respondents. If people derive utility from saying they are willing to pay for a public good (social desirability bias or warm glow), this potentially drives a wedge between people’s stated value for a good in a survey and people’s value for a good provided to them from the government. Tax payments are more binding than out-of-pocket payments. Payment towards public health programs via income tax may therefore generate lower consumer surplus than if the intervention was financed out-of-pocket with the option of opting out both in terms of participation as well as financially. Finally, only a few studies have looked at the impact of frequency of payments. The effect of temporal framing is clearly potentially important and at the same time an unavoidable component of the payment vehicle, yet it remains at present unexplored