This note sets out one possible, simple algorithm approach for ensuring fairer, more gender-balanced panels for institutional arbitration for individual cases, and averaged across an institution's case portfolio, as follows:For single arbitrator cases, each party 1st agrees on one provisional male candidate and one provisional female candidate. The single arbitrator would then be chosen from this short-list of 2, by the arbitral institution, using an independent fair, random, "coin-toss" type mechanism. The gender split per single case would always be 100% to 0% randomly either way.For 3 member panels, each party appoints an arbitrator. If both of these arbitrators have the same gender then the new rules mandate that they have to appoint a presiding arbitrator of the other gender. In such a case the final gender split will always be: 66.7% to 33.3% either way.For 5 member panels, each party is invited to appoint 2 arbitrators, one of each gender. If all 4 arbitrators appointed are one gender then one from each side is rejected and their appointment process repeated, more than once if necessary. When this process stops then if the party appointed arbitrators are now gender-balanced, then any presiding arbitrator can be chosen. Whereas if the party-appointed arbitrators are still unbalanced: 3:1, then the presiding arbitrator chosen must be the minority gender on the panel. In such a case the final split will always be: 60% to 40% either way.(For any larger odd-number panels, a similar method as for 5 member panels would be used, mutatis mutandis.)In the case of arbitration panelists whose defined gender is different from that assigned at birth, then a flexible approach should be taken in accordance with their wishes.N.B. When applied to all an arbitration institution's new cases, the gender ratio for arbitrator panel appointees would be expected to move progressively closer to 50% : 50% over time.Currently, because arbitrators appointed tend to be older generation and experienced, this favors male arbitrators and all male arbitrator panels and arguably excludes female arbitrator candidates from being appointed and sometimes even from "getting a first foot on the ladder". However with high relative proportions of both female lawyer recruits and law firm partners coming through, it is quite possible that this situation could suddenly reverse in future to favor female arbitrators and all female arbitrator panels and arguably exclude other good arbitrator candidates instead.The suggested new algorithm and proposed new institutional rule changes above should help ensure fairer and more even representation of all genders on arbitration panels both now and in future, irrespective of background market conditions, for as long that is as good human arbitration panel members (rather than say non-human AGI systems) are required.The paper also calculates quantitative estimates of the likely impact on arbitration panel composition of applying these rules on either a mandatory or voluntary basis, and a draft memorandum setting out the proposed rules, that could be adopted by arbitration institutions or by parties and law firms between themselves.Similar new rebalancing rules could also be applied to foster and encourage more racial and cultural diversity on arbitrator panels and this is an additional challenge that arguably needs to be tackled too