As delineated now, once both sides of an appeal are funded, the disputes jumps right into the voting phase.
This does not make any sense, since there is not enough time for any of the sides to present further evidence or contest the decisions of the previous jurors. It does not follow what regular courts do when there is an appeal to a ruling.
I believe that there should be a new evidence period for each round of appeals.
From the General Court policy, this is the rationale:
Court Purpose
[…] To ensure fairness to jurors who vote at different times within a voting period, jurors should disregard any evidence that is both 1) submitted after the end of the evidence period of the initial round of a dispute AND 2) cannot be reasonably considered to have been readily, publicly available to jurors. Jurors may, however, consider arguments that are submitted later that are based upon existing evidence and/or information which a juror considering the case during the evidence period of the initial round could reasonably have been expected to find themselves. (Ex: a party submits a new photo of a damaged product in an insurance case after the evidence period; this photo should not be considered by jurors. Ex: in a dispute over whether a token satisfies the criteria of a curated list of ERC20 tokens, an argument that reminds jurors of a definitional element of the ERC20 standard is submitted; this is publicly available and can be considered by jurors. Ex: in a dispute over whether a token satisfies a decentralization criterion for an exchange listing, an argument that invokes the distribution of tokens over different Ethereum addresses, as publicly available from sites such as Etherscan, can be considered by jurors.). […]
From the Kleros perspective, if you think that currently the voting period doesn’t provide enough time to debate the cases, then what should be done is increase said period. I personally would consider decreasing both the evidence and the voting periods.