The budget challenge this autumn, clarity about what the Social Democrats' leadership wants going forward and the ability to enthuse within the party.
There are probable demands on who will take over after Stefan Löfven according to SVT's political expert.
C and L may make new demands before a new Prime Minister's vote in the Riksdag - therefore the new leader must be able to compromise with them.
At the same time, there is a will within the party to go more to the left.
- There has long been an internal pressure within the party to turn to the left, especially after all the January cooperation compromises.
I think it will be a clear requirement that you should be clearer with what S really wants and form an opinion for it, says Marmorstein.
"The given candidate"
The starting field is wider now than under the turbulent conditions that prevailed when Stefan Löfven was elected ten years ago.
Many want to see a woman in the post, the Social Democrats have never had a female leader who was also prime minister.
- There is a strong internal pressure that the person must be a woman, competent and well-known among voters.
Magdalena Andersson is the given candidate.
She is more left-wing than her reputation claims, says Marmorstein.
Damberg strong candidate
Others who could be relevant are Minister of Social Affairs Lena Hallengren, EU Commissioner Ylva Johansson and Minister of Labor Eva Nordmark.
If one deviates from the requirement that it must be a woman, the name is mentioned as Minister of Digitization Anders Ygeman.
Minister of Social Insurance Ardalan Shekarabi, Minister of Justice Morgan Johansson and Minister of the Interior Mikael Damberg.
- He is very experienced and has been responsible for a very important issue, gang crime.
It may be that he is considered to be on the right, but he is one of those who is best placed.
Hear more about which top names it is speculated about, in the clip above.