Erik Voeten links to Charles Mann's article which is about, in Voeten's words, "the potential deleterious consequences of finding large quantities of natural gas (methane hydrate) underneath the seafloor." Voeten's post and Mann's article suggest that among these consequences could be increased political instability, as regimes now propped up by oil become weaker and -- this point is the one Voeten stresses -- as countries become less dependent on oil imports. Dependence on oil imports makes the dependent countries co-operative and leads them to behave like good international citizens, lest turmoil interfere with the international flow of petroleum on which they rely: so say Voeten and Michael Ross in a paper on SSRN to which Voeten links.
Having only skimmed Mann's article, my off-the-cuff reaction is that the more serious potential deleterious effect of methane hydrate discoveries is that they will slow down the shift to renewable energy sources (solar and wind). Mann mentions this at the end of his piece. That seems like a fairly certain consequence of new natural gas discoveries, whereas the argument about political consequences seems somewhat more speculative to me. For instance, I doubt that its current oil-dependence has all that much of a constraining effect on U.S. foreign policy. YMMV.