It is well known that any higher-order Markov chain can be associated with a first-order Markov chain. In this primarily expository article, we present the first fairly comprehensive analysis of the relationship between higher-order and first-order Markov chains, together with illustrative examples. Our main objective is to address the central question as posed in the title.

This article argues that identificational focus, which expresses exhaustive identification and occupies the specifier of a functional projection, must be distinguished in language description from information focus, which conveys new information and involves no syntactic reordering. The properties of the two types of focus are established on the basis of Hungarian and English material. It is argued that the cleft constituent is the realization of identificational focus in English. Only-phrases are analyzed as identificational foci carrying an evaluative presupposition. The feature specification of identificational focus is shown to be subject to parametric variation: the focus operators of various languages are specified for the positive value of either or both of the features [+exhaustive] and [+contrastive].

Health technology assessment (HTA) processes provide evidence to inform the supply of healthcare, often comparing results from economic evaluation to a policy threshold to judge cost-effectiveness. However, recommended policy thresholds may not always align with empirical estimates of the opportunity costs of health care expenditure, captured by marginal productivity of healthcare expenditure (‘k’). Such estimates are needed to inform the net health impact of funding decisions. We map policy thresholds in HTA guidelines against published estimates of k. We extract information from HTA guidelines identified in a previous literature review, including recommended perspective, relevant costs and outcomes, and justification for the threshold. Studies estimating k were obtained from a separate review. Of the 47 included HTA guidelines, 20 state an explicit policy threshold and 12 justify their choice. Estimates of k were available for 13 countries. Among the eight countries with explicit policy thresholds and k estimates, three matched. The recommended perspective influences whether k alone is sufficient or appropriate to inform cost-effectiveness judgements. It is important that guideline setters are aware of empirical estimates of k; and that economic evaluations consider k to reflect health opportunity costs even where the policy threshold is justified on other grounds.

This article presents a typology of consonant harmony or LONG DISTANCE CONSONANT AGREEMENT that is analyzed as arising through correspondence relations between consonants rather than feature spreading. The model covers a range of agreement patterns (nasal, laryngeal, liquid, coronal, dorsal) and offers several advantages. Similarity of agreeing consonants is central to the typology and is incorporated directly into the constraints driving correspondence. Agreement by correspondence without feature spreading captures the neutrality of intervening segments, which neither block nor undergo. Case studies of laryngeal agreement and nasal agreement are presented, demonstrating the model's capacity to capture varying degrees of similarity crosslinguistically.