Well, Polycarp, the composition of the Lords is all a bit complicated, but here goes.
There are currently five categories of members of the House of Lords.
Life peers. Individuals granted peerages for life. Appointments are made on the recommendation of the Prime Minister, although by convention he/she includes some names recommended by the other party leaders. There is no limit to the number that can be created. There are currently about 560 of them, of whom about 50 have been created since the beginning of this year alone.
Law lords. Senior judges who carry out the judicial functions of the House of Lords. Although they cannot hear appeals once they reach the age of 75, they continue sitting as peers until their deaths so they are, in effect, another type of life peer.
Archbishops and Bishops. The 26 most senior Anglican bishops. The most senior of all automatically get seats, while the others are appointed on the basis of length of service. They cease to sit when they retire, although retiring Archbishops of Canterbury conventionally get a life peerage.
The 90 hereditary peers retained under the 1999 reform. This is where it gets really complicated. These 90 peers were elected from among those who sat in the Lords at the time of the 1999 reform. Each of the major parties, plus the crossbenchers, were allocated a share of these 90 seats according to the affiliations of the hereditary peers at the time of the reform. The peers of each party then held ballots to determine which of them were to get them. In practice, this meant that the more active peers survived the purge. These 90 peers will continue to hold these seats until such time as the second stage of Lords reform takes place, although it is still not clear what and what that second stage will be. Conceivably they could retain these seats indefinitately. Provision was made for by-elections to be held in the event of those peers dying and such a by-election has already been held. It has been pointed out that these elections involve some of the smallest electorates for seats in the parliamentary assembly of any Western democracy.
Defining exactly who sat as hereditary peers before 1999 is also difficult as there were all sorts of weird exceptions and anomalies. Most however were titles which passed to each successive male heir of the person to whom it had originally been granted.
- Great officers. The Earl Marshal and the Lord Great Chamberlain (both of which are hereditary offices) also retained their seats under the 1999 reform, ostensibly because they take part in certain ceremonies involving the House. Both the current holders have avoided any other involvement in its proceedings since then.
As for the Halifax title, it was only a viscountcy, not a marquisate. Other cases of the heirs to peerages being granted peerages in their own right were not completely unknown. More common, however, were cases of the heirs to dukedoms, marquisates or earldoms being summoned by virtue of one of their father’s lesser titles. The obvious modern example was Lord Cranborne, the peer who brokered the 1999 deal with Blair. He had been summoned in the viscountcy of his father, the Marquis of Salisbury.
The really peculiar cases are when an eldest son inherits a peerage during his father’s lifetime. This can happen in those rare cases when a peerage can pass through a female line.
As for aristocrats choosing not to use their titles, it all depends on the individual and the specific context. The current example that immediately springs to mind would be ‘Michael Ancram’, the Deputy Leader and Foreign Affairs spokesman of the Conservatives in the Commons, who is actually the Earl of Ancram. He calculated, probably correctly, that using his title would have harmed his political career, even in the Conservative party. That he had a title was one reason why he did so badly when he tried standing for the party leadership.