From this wiki page:

WPA and WPA2 use keys derived from an EAPOL handshake to encrypt
traffic. Unless *all four* handshake packets are present for the
session you're trying to decrypt, Wireshark won't be able to
decrypt the traffic. You can use the display filter eapol to
locate EAPOL packets in your capture.

I've noticed that it works with (1,2,4) too. Can someone please explain this?

Test case

This is the gzipped handshake (1, 2, 4) and an ecrypted ARP packet (SSID: SSID, password: password) in base64 encoding:

H4sICEarjU8AA2hhbmRzaGFrZS5jYXAAu3J400ImBhYGGPj/n4GhHkhfXNHr37KQgWEqAwQzMAgx
6HkAKbFWzgUMhxgZGDiYrjIwKGUqcW5g4Ldd3rcFQn5IXbWKGaiso4+RmSH+H0MngwLUZMarj4Rn
S8vInf5yfO7mgrMyr9g/Jpa9XVbRdaxH58v1fO3vDCQDkCNv7mFgWMsAwXBHMoEceQ3kSMZbDFDn
ITk1gBnJkeX/GDkRjmyccfus4BKl75HC2cnW1eXrjExNf66uYz+VGLl+snrF7j2EnHQy3JjDKPb9
3fOd9zT0TmofYZC4K8YQ8IkR6JaAT0zIJMjxtWaMmCEMdvwNnI5PYEYJYSTHM5EegqhggYbFhgsJ
9gJXy42PMx9JzYKEcFkcG0MJULYE2ZEGrZwHIMnASwc1GSw4mmH1JCCNQYEF7C7tjasVT+0/J3LP
gie59HFL+5RDIdmZ8rGMEldN5s668eb/tp8vQ+7OrT9jPj/B7425QIGJI3Pft72dLxav8BefvcGU
7+kfABxJX+SjAgAA

Decode with:

$ base64 -d | gunzip > handshake.cap

Run tshark to see if it correctly decrypt the ARP packet:

$ tshark -r handshake.cap -o wlan.enable_decryption:TRUE -o wlan.wep_key1:wpa-pwd:password:SSID

It should print:

  1   0.000000 D-Link_a7:8e:b4 -> HonHaiPr_22:09:b0 EAPOL Key
  2   0.006997 HonHaiPr_22:09:b0 -> D-Link_a7:8e:b4 EAPOL Key
  3   0.038137 HonHaiPr_22:09:b0 -> D-Link_a7:8e:b4 EAPOL Key
  4   0.376050 ZyxelCom_68:3a:e4 -> HonHaiPr_22:09:b0 ARP 192.168.1.1 is at 00:a0:c5:68:3a:e4