The threshold is low---there just needs to be one country to halt the entire process.
Martin Jelsma 18, Director of the Drugs and Democracy Programme, Transnational Institute, Senior Research Associate at the Global Drug Policy Observatory (GDPO) at Swansea University; Neil Boister, Professor of International Law at the University of Canterbury; David Bewley-Taylor, Professor of International Relations and Public Policy, Director of the GDPO; Malgosia Fitzmaurice, Professor of Public International Law at Queen Mary University of London; John Walsh, Director for Drug Policy and the Andes at the Washington Office on Latin America, March 2018, “Balancing Treaty Stability and Change: Inter se modification of the UN drug control conventions to facilitate cannabis regulation,” WOLA, Policy Report 7, https://www.wola.org/wp-content/uploads/2018/04/FINAL_Updated.pdf, kav
Similarly, procedures within all three treaties allow even limited opposition to a proposed amendment to thwart the initiative. For both the 1961 and 1971 Conventions, if no Party rejects the amendment within 18 months after circulation ‘it shall thereupon enter into force.’ (Article 47 (2) and Article 30 (2) respectively). However, if a proposed amendment is rejected by one or more parties, the Council may follow suit in ‘response to objections and the substantial arguments provided’67 or decide whether a conference should be called to consider the amendment. As well as operating on a more generous timetable, provisions within the 1988 Convention differ somewhat in other respects. According to Article 31 (1), if a proposed and circulated amendment has not been rejected by any party within 24 months, ‘it shall be deemed to have been accepted and shall enter into force in respect of a Party…’ However, moving away from ‘tacit approval’ within the earlier treaties,68 this comes into effect ninety days after ‘that party has deposited with the Secretary General an instrument expressing its consent to be bound by that amendment.’ In this case, if the proposed amendment is rejected by any party, the UNSG must consult with the parties and ‘if a majority so requests, bring the matter to the Council which may decide to call a conference.’ (Article 31 (2))