A short note on the joint entropy of n/2-wise independence

In this note, we prove a tight lower bound on the joint entropy of $n$ unbiased Bernoulli random variables which are $n/2$-wise independent. For general $k$-wise independence, we give new lower bounds by adapting Navon and Samorodnitsky's Fourier proof of the `LP bound' on error correcting codes. This counts as partial progress on a problem asked by Gavinsky and Pudl\'ak.Comment: 6 pages, some errors fixe

Independent Sector Regulators and their Relationship with Competition Authorities

Independent sector regulators and competition authorities share many objectives and common interests, particularly because they both can play key roles in promoting effective and beneficial competition. In this note, the criteria and rationale for the independence of sector regulators and competition authorities are explained, along with a suggestion that independence may sometimes be especially critical for institutions with broad economic oversight and quasi-judicial responsibilities or, alternately, for institutions most subject to influence of special interests. The note suggests that sector regulators may benefit, in times of high technological change and uncertainty, from principle-based laws that allow regulators the flexibility to adjust their precise rules in light of evolving circumstances. Moreover, the note suggests that in some respects, the sectors subject to independent regulation may usefully include other sectors beyond those most traditionally associated with independent regulation. Ultimately, ensuring consistency and convergence between sector regulator and competition authority objectives and actions is important; ironically, independence can make ensuring such consistency through direct co-operation a challenge. Based on international experience, multiple mechanisms exist for achieving or encouraging such consistency; some combination of these merits consideration by designers of competition policy regimes