What's a degree "by resolution"?
Basically, it's a "free masters degree" to members who otherwise don't qualify for the masters degree, for various reasons.  

Here it is, direct from Oxford:


  Conferment of Degrees
  7.1. The procedures for the conferment, both at the Encaenia and on other occasions, of Degrees by Diploma, Honorary Degrees, Ordinary
  Degrees, and Degrees by Incorporation shall be determined by
  regulation, and the regulations concerned shall be published from time
  to time in a Handbook for the Conduct of University Ceremonies.
  
  7.2. (1) In the case of a person in any of the categories set out in paragraph (2) below who does not hold, and is not qualified for, any
  of the Degrees (other than Honorary Degrees) of Doctor of Divinity,
  Doctor of Civil Law, Doctor of Medicine, Master of Arts, Master of
  Biochemistry, Master of Chemistry, Master of Earth Sciences, Master of
  Engineering, Master of Mathematics, or Master of Physics of the
  University, Council shall as soon as possible propose to Congregation
  that a Degree of Master of Arts by Resolution be conferred upon that
  person without fee, if (and only if) he or she holds both a bachelor’s
  and a doctor’s degree (other than an honorary degree) of any
  university or universities or of any such other institution or
  institutions as Council may determine by regulation from time to time,
  or that at least twenty terms have lapsed since he or she first became
  a member of a university or such other institution, or, in the case of
  a person who is not a member of any university, that he or she is at
  least 25 years of age.
  
  (2) The categories referred to in paragraph (1) above are:
  
  (a) the Chancellor;
  
  (b) the High Steward;
  
  (c) the Vice-Chancellor;
  
  (d) the Proctors;
  
  (e) the heads of all the colleges, societies, and Permanent Private
  Halls included in Statute V;
  
  (f) the members of the governing bodies of all the colleges and
  societies included in Statute V (but not of the Permanent Private
  Halls);
  
  (g) the principal bursar or treasurer of each of the colleges and
  societies included in Statute V (but not of the Permanent Private
  Halls), if he or she is not a member of its governing body.
  
  (3) In the case of a person excluded because none of the conditions in
  paragraphs (1) and (2) above is met, Council shall proceed as soon as
  possible after one of them has been met.
  
  (4) Nothing in this regulation shall restrict the power of Council to
  propose to Congregation that a Degree by Resolution be conferred
  without fee upon any person it considers appropriate.
  
  7.3. A Degree by Resolution shall be deemed to have been conferred with effect from the approval of the resolution by Congregation.