Concerning the numbering of locants for substituents, the most important simplified criteria are:

1. lower locants for the principal characteristic group that is expressed as suffix
2. lower locants for prefixes
3. lower locants for substituents cited first as a prefix in the name

The corresponding actual wording in the current version of Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book) reads as follows:

P-14.4 NUMBERING

 

When several structural features appear in cyclic and acyclic compounds, low locants are assigned to them in the following decreasing order of seniority:

 

(…)

 

(c) principal characteristic groups and free valences (suffixes);

 

(…)

 

(f) detachable alphabetized prefixes, all considered together in a series of increasing numerical order;

 

(g) lowest locants for the substituent cited first as a prefix in the name;

 

(…)

The $\ce{-OH}$ group is the principal characteristic group in this case. It is expressed as suffix ‘ol’.

Therefore, low locants are assigned first to the $\ce{-OH}$ groups according to Rule (c), which yields ethane-1,1-diol.

After that, a low locant is assigned to the chloro groups according to Rule (f); however, the only possible numbering left is 2,2,2-trichloroethane-1,1-diol.

Concerning the numbering of locants for substituents, the most important simplified criteria are:

1. lower locants for the principal characteristic group that is expressed as suffix
2. lower locants for prefixes
3. lower locants for substituents cited first as a prefix in the name

The corresponding actual wording in the current version of Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book) reads as follows:

P-14.4 NUMBERING

When several structural features appear in cyclic and acyclic compounds, low locants are assigned to them in the following decreasing order of seniority:

(…)

(c) principal characteristic groups and free valences (suffixes);

(…)

(f) detachable alphabetized prefixes, all considered together in a series of increasing numerical order;

(g) lowest locants for the substituent cited first as a prefix in the name;

(…)

The $\ce{-OH}$ group is the principal characteristic group in this case. It is expressed as suffix ‘ol’.

Therefore, low locants are assigned first to the $\ce{-OH}$ groups according to Rule (c), which yields ethane-1,1-diol.

After that, a low locant is assigned to the chloro groups according to Rule (f); however, the only possible numbering left is 2,2,2-trichloroethane-1,1-diol.