Issue at hand:
Rival factions are staking claim to the name and symbol of the Samajwadi Party. How does the Election Commission decide which group or faction is the real party? 

Under what authority does the EC decide such disputes?
The Election Symbols (Reservation and Allotment) Order, 1968 empowers the EC to recognise political parties and allot symbols. Under Paragraph 15 of the Order, it can decide disputes among rival groups or sections of a recognised political party staking claim to its name and symbol.

What is the legal status of Paragraph 15?
Under Paragraph 15, the EC is the only authority to decide issues on a dispute or a merger. The Supreme Court upheld its validity in Sadiq Ali and another vs. ECI in 1971.
What aspects does the EC consider before recognising one group as the official party?
The ECI primarily ascertains the support enjoyed by a claimant within a political party in its organisational wing and in its legislative wing.

How does the ECI establish a claim of majority in these wings?
The Commission examines the party’s constitution and its list of office-bearers submitted when the party was united. It identifies the apex committee(s) in the organisation and finds out how many office-bearers, members or delegates support the rival claimants. 
For the legislative wing, the party goes by the number of MPs and MLAs in the rival camps. It may consider affidavits filed by these members to ascertain where they stand.

What ruling will the EC give after a definite finding?
The ECI may decide the dispute in favour of one faction by holding that it commands enough support in its organisational and legislative wings to be entitled to the name and symbol of the recognised party. It may permit the other group to register itself as a separate political party.

What happens when there is no certainty about the majority of either faction?
Where the party is either vertically divided or it is not possible to say with certainty which group has a majority, the EC may freeze the party’s symbol and allow the groups to register themselves with new names or add prefixes or suffixes to the party’s existing names.

Can the dispute relating to SP be decided immediately, given that elections are round the corner?
The EC may take time to gather enough material to decide the question. For immediate electoral purposes, it may freeze the party’s symbol and advise the groups to fight the elections in different names and on temporary symbols.

What happens when rival factions settle their differences in future?
If reunited, the claimants may approach the EC again and seek to be recognised as a unified party. The EC is also empowered to recognise mergers of groups into one entity. It may restore the symbol and name of the original party.