IN the final election tally, the long-ruling Liberal Democratic Party was granted its wish - it will have as many seats in the new House of Representatives as it had in the old. The LDP actually won 223 seats yesterday, but informed sources in Tokyo indicate that at least four of the 30 independents and minor party victors in the election are ready to cross over to the LDP, thus restoring its strength to the 227 total it had in the dissolved House. The three new political parties made up largely of LDP dissidents won 103 seats all together. So, in one sense, the LDP and its breakaways - the total conservative membership in the new house - make a total of 330, better than any performamnce by the LDPwhen it was still united. The coalition-building arithmetic which will now dominate Japanese politics is complex. With the four assured crossovers, the LDP needs 29 more seats to gain a simple majority of 256, and 44 more seats to get a working majority of 271 capable of controlling parliament. The five opposition parties which have discussed a coalition - Shinseito, the Socialists, the Democratic Socialists, Komeito, and the Salaryman's Party - only won 195 seats. Even if they persuade the other two new parties - Nihon Shinto and Sakigake - to join them, the seven-party coalition would still only have 243 seats. In order to get a simple majority the opposition coalition would either have to attract many independents, or think the previously unthinkable, and ask the 15 communist members to join in. All such calculations fall by the wayside, however, when a further complication is brought into the political calculus: both the Japan Socialists and the LDP may now begin to break up. Shinseito leader, and former LDP secretary-general, Ichiro Ozawa is sure to be busy trying to win more LDP dissidents from those in the party favouring reform. In the case of the socialists, their worst-ever defeat may bring to a head the longstanding conflict between the party's extreme ideological left, and the more moderate democratic socialists. The latter favour joining up with Mr Ozawa while the former donot like the idea. A far-reaching change in the contours of Japanese politics could be in prospect.