user5406: I've read that it encourages users to consolidate UTXO sets. How would it be doing that?

user120: Witnesses do not need to be stored once they have been verified and can be discarded. This effectively reduces the size of the UTXO. The discount is supposed to account for the reduced storage requirements and to encourage users to switch to segwit, benefiting the network as a whole. 

user5292: Because Txouts are about 1/4th the size of TxIns, since signatures are that much bigger than a simple hash.
This means that in the old situation it was cheaper to split coins (increasing UTXO set size and creating more dust) than to merge them (decreasing UTXO set size).
With this discount, the playing field is leveled so that when the wallet has a choice, it will not favour UTXO increase.
Adam Back:
https://www.reddit.com/r/Bitcoin/comments/4d3pdg/clearing_the_fud_around_segwit/d1o12q1
Gregory Maxwell:
https://www.reddit.com/r/Bitcoin/comments/4d3pdg/clearing_the_fud_around_segwit/d1ns0bo

user18196: A transaction input means that the previous output it is spending can be removed from the expensive UTXO set. To incentivize making txin's (and hence reducing the UTXO size), Segregated witness includes a change to count the size of transaction input scripts as 1/4 the number of bytes that it actually consumes. 
Transactions typically compete for block space by attempting to have a high ratio of fees to byte size in the block. By counting the bytes from inputs as 1/4 of the actual bytes the inputs consume, it makes transactions with more inputs more competitive in having a high fee to size ratio. Hence, the change in counting input data size incentivizes transaction makers to spend more inputs by essentially requiring less in fees. 
It should be noted that although spending more inputs makes the UTXO set smaller in size, it also associates some outputs (addresses) as likely being owned by the same user. So there is a privacy/cost trade off for the user. 
Additionally, another reason that the witness data is discounted is that it presents an opportunity to increase the block size as a soft fork. 

5406: <p>I've read that it encourages users to consolidate UTXO sets. How would it be doing that?</p>
 120: <p>Witnesses do not need to be stored once they have been verified and can be discarded. This effectively reduces the size of the UTXO. The discount is supposed to account for the reduced storage requirements and to encourage users to switch to segwit, benefiting the network as a whole. </p>
 5292: <p>Because Txouts are about 1/4th the size of TxIns, since signatures are that much bigger than a simple hash.</p>

<p>This means that in the old situation it was cheaper to split coins (increasing UTXO set size and creating more dust) than to merge them (decreasing UTXO set size).</p>

<p>With this discount, the playing field is leveled so that when the wallet has a choice, it will not favour UTXO increase.</p>

<p>Adam Back:</p>

<p><a href="https://www.reddit.com/r/Bitcoin/comments/4d3pdg/clearing_the_fud_around_segwit/d1o12q1" rel="nofollow">https://www.reddit.com/r/Bitcoin/comments/4d3pdg/clearing_the_fud_around_segwit/d1o12q1</a></p>

<p>Gregory Maxwell:</p>

<p><a href="https://www.reddit.com/r/Bitcoin/comments/4d3pdg/clearing_the_fud_around_segwit/d1ns0bo" rel="nofollow">https://www.reddit.com/r/Bitcoin/comments/4d3pdg/clearing_the_fud_around_segwit/d1ns0bo</a></p>
 18196: <p>A transaction input means that the previous output it is spending can be removed from the expensive UTXO set. To incentivize making txin's (and hence reducing the UTXO size), Segregated witness includes a change to count the size of transaction input scripts as 1/4 the number of bytes that it actually consumes. </p>

<p>Transactions typically compete for block space by attempting to have a high ratio of fees to byte size in the block. By counting the bytes from inputs as 1/4 of the actual bytes the inputs consume, it makes transactions with more inputs more competitive in having a high fee to size ratio. Hence, the change in counting input data size incentivizes transaction makers to spend more inputs by essentially requiring less in fees. </p>

<p>It should be noted that although spending more inputs makes the UTXO set smaller in size, it also associates some outputs (addresses) as likely being owned by the same user. So there is a privacy/cost trade off for the user. </p>

<p>Additionally, another reason that the witness data is discounted is that it presents an opportunity to increase the block size as a soft fork. </p>
